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Journal articles on the topic 'Quantum channels on a graph state'

Author: Grafiati

Published: 6 September 2023

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1

Liao, Longxia, Xiaoqi Peng, Jinjing Shi, and Ying Guo. "Graph state-based quantum authentication scheme." International Journal of Modern Physics B 31, no. 09 (April 10, 2017): 1750067. http://dx.doi.org/10.1142/s0217979217500679.

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Inspired by the special properties of the graph state, a quantum authentication scheme is proposed in this paper, which is implemented with the utilization of the graph state. Two entities, a reliable party, Trent, as a verifier and Alice as prover are included. Trent is responsible for registering Alice in the beginning and confirming Alice in the end. The proposed scheme is simple in structure and convenient to realize in the realistic physical system due to the use of the graph state in a one-way quantum channel. In addition, the security of the scheme is extensively analyzed and accordingly can resist the general individual attack strategies.

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2

Honrubia, Efrén, and Ángel S. Sanz. "Graph Approach to Quantum Teleportation Dynamics." Quantum Reports 2, no. 3 (July 10, 2020): 352–77. http://dx.doi.org/10.3390/quantum2030025.

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Quantum teleportation plays a key role in modern quantum technologies. Thus, it is of much interest to generate alternative approaches or representations that are aimed at allowing us a better understanding of the physics involved in the process from different perspectives. With this purpose, here an approach based on graph theory is introduced and discussed in the context of some applications. Its main goal is to provide a fully symbolic framework for quantum teleportation from a dynamical viewpoint, which makes explicit at each stage of the process how entanglement and information swap among the qubits involved in it. In order to construct this dynamical perspective, it has been necessary to define some auxiliary elements, namely virtual nodes and edges, as well as an additional notation for nodes describing potential states (against nodes accounting for actual states). With these elements, not only the flow of the process can be followed step by step, but they also allow us to establish a direct correspondence between this graph-based approach and the usual state vector description. To show the suitability and versatility of this graph-based approach, several particular teleportation examples are examined in detail, which include bipartite, tripartite, and tetrapartite maximally entangled states as quantum channels. From the analysis of these cases, a general protocol is devised to describe the sharing of quantum information in presence of maximally entangled multi-qubit system.

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3

Piveteau, Christophe, and Joseph M. Renes. "Quantum message-passing algorithm for optimal and efficient decoding." Quantum 6 (August 23, 2022): 784. http://dx.doi.org/10.22331/q-2022-08-23-784.

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Recently, Renes proposed a quantum algorithm called belief propagation with quantum messages (BPQM) for decoding classical data encoded using a binary linear code with tree Tanner graph that is transmitted over a pure-state CQ channel \cite{renes_2017}, i.e., a channel with classical input and pure-state quantum output. The algorithm presents a genuine quantum counterpart to decoding based on the classical belief propagation algorithm, which has found wide success in classical coding theory when used in conjunction with LDPC or Turbo codes. More recently Rengaswamy etal. \cite{rengaswamy_2020} observed that BPQM implements the optimal decoder on a small example code, in that it implements the optimal measurement that distinguishes the quantum output states for the set of input codewords with highest achievable probability. Here we significantly expand the understanding, formalism, and applicability of the BPQM algorithm with the following contributions. First, we prove analytically that BPQM realizes optimal decoding for any binary linear code with tree Tanner graph. We also provide the first formal description of the BPQM algorithm in full detail and without any ambiguity. In so doing, we identify a key flaw overlooked in the original algorithm and subsequent works which implies quantum circuit realizations will be exponentially large in the code dimension. Although BPQM passes quantum messages, other information required by the algorithm is processed globally. We remedy this problem by formulating a truly message-passing algorithm which approximates BPQM and has quantum circuit complexity O(poly n,polylog 1ϵ), where n is the code length and ϵ is the approximation error. Finally, we also propose a novel method for extending BPQM to factor graphs containing cycles by making use of approximate cloning. We show some promising numerical results that indicate that BPQM on factor graphs with cycles can significantly outperform the best possible classical decoder.

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4

Lowe, Angus, Matija Medvidović, Anthony Hayes, Lee J. O'Riordan, Thomas R. Bromley, Juan Miguel Arrazola, and Nathan Killoran. "Fast quantum circuit cutting with randomized measurements." Quantum 7 (March 2, 2023): 934. http://dx.doi.org/10.22331/q-2023-03-02-934.

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We propose a new method to extend the size of a quantum computation beyond the number of physical qubits available on a single device. This is accomplished by randomly inserting measure-and-prepare channels to express the output state of a large circuit as a separable state across distinct devices. Our method employs randomized measurements, resulting in a sample overhead that is O~(4k/ε2), where ε is the accuracy of the computation and k the number of parallel wires that are "cut" to obtain smaller sub-circuits. We also show an information-theoretic lower bound of Ω(2k/ε2) for any comparable procedure. We use our techniques to show that circuits in the Quantum Approximate Optimization Algorithm (QAOA) with p entangling layers can be simulated by circuits on a fraction of the original number of qubits with an overhead that is roughly 2O(pκ), where κ is the size of a known balanced vertex separator of the graph which encodes the optimization problem. We obtain numerical evidence of practical speedups using our method applied to the QAOA, compared to prior work. Finally, we investigate the practical feasibility of applying the circuit cutting procedure to large-scale QAOA problems on clustered graphs by using a 30-qubit simulator to evaluate the variational energy of a 129-qubit problem as well as carry out a 62-qubit optimization.

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5

Erementchouk, Mikhail, and Michael N. Leuenberger. "Entanglement Dynamics of Second Quantized Quantum Fields." ISRN Mathematical Physics 2014 (January 28, 2014): 1–19. http://dx.doi.org/10.1155/2014/264956.

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We study the entanglement dynamics in the system of coupled boson fields. We demonstrate that there are different natural notions of locality in this context leading to inequivalent notions of entanglement. We concentrate on the particle picture, when entanglement of one particle is determined by one-particle density matrix. We study, in detail, the effect of interaction preserving populations of individual one-particle states. We show that if the system is initially in a disentangled state with the definite total number of particles and the dimension of the one-particle Hilbert space is more than two, then only potentials of the special form admit complete entanglement, which is shown to be reached at NOON states. If the system is initially in Glauber’s coherent state, complete entanglement is not reached despite the presence of two entangling channels in this case. We conclude with studying the time evolution of entanglement of photons in a cavity with multiple quantum dots in the limit of large number of photons. We show that in a relatively short time scale the completely entangled states belong to the class of graph states and are formed due to the interaction with dots in resonance with the cavity modes.

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6

Colafranceschi, Eugenia, and Gerardo Adesso. "Holographic entanglement in spin network states: A focused review." AVS Quantum Science 4, no. 2 (June 2022): 025901. http://dx.doi.org/10.1116/5.0087122.

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In the long-standing quest to reconcile gravity with quantum mechanics, profound connections have been unveiled between concepts traditionally pertaining to a quantum information theory, such as entanglement, and constitutive features of gravity, like holography. Developing and promoting these connections from the conceptual to the operational level unlock access to a powerful set of tools which can be pivotal toward the formulation of a consistent theory of quantum gravity. Here, we review recent progress on the role and applications of quantum informational methods, in particular tensor networks, for quantum gravity models. We focus on spin network states dual to finite regions of space, represented as entanglement graphs in the group field theory approach to quantum gravity, and illustrate how techniques from random tensor networks can be exploited to investigate their holographic properties. In particular, spin network states can be interpreted as maps from bulk to boundary, whose holographic behavior increases with the inhomogeneity of their geometric data (up to becoming proper quantum channels). The entanglement entropy of boundary states, which are obtained by feeding such maps with suitable bulk states, is then proved to follow a bulk area law with corrections due to the entanglement of the bulk state. We further review how exceeding a certain threshold of bulk entanglement leads to the emergence of a black hole-like region, revealing intriguing perspectives for quantum cosmology.

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7

Bannink, Tom, Jop Briët, Farrokh Labib, and Hans Maassen. "Quasirandom quantum channels." Quantum 4 (July 16, 2020): 298. http://dx.doi.org/10.22331/q-2020-07-16-298.

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Mixing (or quasirandom) properties of the natural transition matrix associated to a graph can be quantified by its distance to the complete graph. Different mixing properties correspond to different norms to measure this distance. For dense graphs, two such properties known as spectral expansion and uniformity were shown to be equivalent in seminal 1989 work of Chung, Graham and Wilson. Recently, Conlon and Zhao extended this equivalence to the case of sparse vertex transitive graphs using the famous Grothendieck inequality. Here we generalize these results to the non-commutative, or `quantum', case, where a transition matrix becomes a quantum channel. In particular, we show that for irreducibly covariant quantum channels, expansion is equivalent to a natural analog of uniformity for graphs, generalizing the result of Conlon and Zhao. Moreover, we show that in these results, the non-commutative and commutative (resp.) Grothendieck inequalities yield the best-possible constants.

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8

Li, Si-Chen, Bang-Ying Tang, Han Zhou, Hui-Cun Yu, Bo Liu, Wan-Rong Yu, and Bo Liu. "First Request First Service Entanglement Routing Scheme for Quantum Networks." Entropy 24, no. 10 (October 1, 2022): 1404. http://dx.doi.org/10.3390/e24101404.

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Quantum networks enable many applications beyond the reach of classical networks by supporting the establishment of long-distance entanglement connections, and are already stepped into the entanglement distribution network stage. The entanglement routing with active wavelength multiplexing schemes is urgently required for satisfying the dynamic connection demands of paired users in large-scale quantum networks. In this article, the entanglement distribution network is modeled into a directed graph, where the internal connection loss among all ports within a node is considered for each supported wavelength channel, which is quite different to classical network graphs. Afterwards, we propose a novel first request first service (FRFS) entanglement routing scheme, which performs the modified Dijkstra algorithm to find out the lowest loss path from the entangled photon source to each paired user in order. Evaluation results show that the proposed FRFS entanglement routing scheme can be applied to large-scale and dynamic topology quantum networks.

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9

Benjamin, Simon C., Daniel E. Browne, Joe Fitzsimons, and John J. L. Morton. "Brokered graph-state quantum computation." New Journal of Physics 8, no. 8 (August 23, 2006): 141. http://dx.doi.org/10.1088/1367-2630/8/8/141.

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10

Antonio, B., D. Markham, and J. Anders. "Adiabatic graph-state quantum computation." New Journal of Physics 16, no. 11 (November 26, 2014): 113070. http://dx.doi.org/10.1088/1367-2630/16/11/113070.

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11

Weaver, Nik. "Quantum Graphs as Quantum Relations." Journal of Geometric Analysis 31, no. 9 (January 13, 2021): 9090–112. http://dx.doi.org/10.1007/s12220-020-00578-w.

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AbstractThe “noncommutative graphs” which arise in quantum error correction are a special case of the quantum relations introduced in Weaver (Quantum relations. Mem Am Math Soc 215(v–vi):81–140, 2012). We use this perspective to interpret the Knill–Laflamme error-correction conditions (Knill and Laflamme in Theory of quantum error-correcting codes. Phys Rev A 55:900-911, 1997) in terms of graph-theoretic independence, to give intrinsic characterizations of Stahlke’s noncommutative graph homomorphisms (Stahlke in Quantum zero-error source-channel coding and non-commutative graph theory. IEEE Trans Inf Theory 62:554–577, 2016) and Duan, Severini, and Winter’s noncommutative bipartite graphs (Duan et al., op. cit. in Zero-error communication via quantum channels, noncommutative graphs, and a quantum Lovász number. IEEE Trans Inf Theory 59:1164–1174, 2013), and to realize the noncommutative confusability graph associated to a quantum channel (Duan et al., op. cit. in Zero-error communication via quantum channels, noncommutative graphs, and a quantum Lovász number. IEEE Trans Inf Theory 59:1164–1174, 2013) as the pullback of a diagonal relation. Our framework includes as special cases not only purely classical and purely quantum information theory, but also the “mixed” setting which arises in quantum systems obeying superselection rules. Thus we are able to define noncommutative confusability graphs, give error correction conditions, and so on, for such systems. This could have practical value, as superselection constraints on information encoding can be physically realistic.

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12

Rangamani, Mukund, and Massimilliano Rota. "Quantum channels in quantum gravity." International Journal of Modern Physics D 23, no. 12 (October 2014): 1442009. http://dx.doi.org/10.1142/s0218271814420097.

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The black hole final state proposal implements manifest unitarity in the process of black hole formation and evaporation in quantum gravity, by postulating a unique final state boundary condition at the singularity. We argue that this proposal can be embedded in the gauge/gravity context by invoking a path integral formalism inspired by the Schwinger–Keldysh like thermo-field double construction in the dual field theory. This allows us to realize the gravitational quantum channels for information retrieval to specific deformations of the field theory path integrals and opens up new connections between geometry and information theory.

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13

Cao, Wei-Feng, Yu-Guang Yang, Dan Li, Jing-Ru Dong, Yi-Hua Zhou, and Wei-Min Shi. "Quantum state transfer on unsymmetrical graphs via discrete-time quantum walk." Modern Physics Letters A 34, no. 38 (December 13, 2019): 1950317. http://dx.doi.org/10.1142/s0217732319503176.

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Perfect state transfer can be achieved between two marked vertices of graphs like a star graph, a complete graph with self-loops and a complete bipartite graph, and two-dimensional Lattice by means of discrete-time quantum walk. In this paper, we investigate the quality of quantum state transfer between two marked vertices of an unsymmetrical graph like the butterfly network. Our numerical results support the conjecture that the fidelity of state transfer depends on the quantum state to be transferred dynamically. The butterfly network is a typical example studied in networking coding. Therefore, these results can provide a clue to the construction of quantum network coding schemes.

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14

Schwarz, Jonathan, Jonas Cassel, Bastian Boll, Martin Gärttner, Peter Albers, and Christoph Schnörr. "Quantum State Assignment Flows." Entropy 25, no. 9 (August 23, 2023): 1253. http://dx.doi.org/10.3390/e25091253.

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This paper introduces assignment flows for density matrices as state spaces for representation and analysis of data associated with vertices of an underlying weighted graph. Determining an assignment flow by geometric integration of the defining dynamical system causes an interaction of the non-commuting states across the graph, and the assignment of a pure (rank-one) state to each vertex after convergence. Adopting the Riemannian–Bogoliubov–Kubo–Mori metric from information geometry leads to closed-form local expressions that can be computed efficiently and implemented in a fine-grained parallel manner. Restriction to the submanifold of commuting density matrices recovers the assignment flows for categorical probability distributions, which merely assign labels from a finite set to each data point. As shown for these flows in our prior work, the novel class of quantum state assignment flows can also be characterized as Riemannian gradient flows with respect to a non-local, non-convex potential after proper reparameterization and under mild conditions on the underlying weight function. This weight function generates the parameters of the layers of a neural network corresponding to and generated by each step of the geometric integration scheme. Numerical results indicate and illustrate the potential of the novel approach for data representation and analysis, including the representation of correlations of data across the graph by entanglement and tensorization.

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15

ANGELES-CANUL, RICARDO JAVIER, RACHAEL M. NORTON, MICHAEL C. OPPERMAN, CHRISTOPHER C. PARIBELLO, MATTHEW C. RUSSELL, and CHRISTINO TAMON. "QUANTUM PERFECT STATE TRANSFER ON WEIGHTED JOIN GRAPHS." International Journal of Quantum Information 07, no. 08 (December 2009): 1429–45. http://dx.doi.org/10.1142/s0219749909006103.

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This paper studies quantum perfect state transfer on weighted graphs. We prove that the join of a weighted two-vertex graph with any regular graph has perfect state transfer. This generalizes a result of Casaccino et al.1 where the regular graph is a complete graph with or without a missing edge. In contrast, we prove that the half-join of a weighted two-vertex graph with any weighted regular graph has no perfect state transfer. As a corollary, unlike for complete graphs, adding weights in complete bipartite graphs does not produce perfect state transfer. We also observe that any Hamming graph has perfect state transfer between each pair of its vertices. The result is a corollary of a closure property on weighted Cartesian products of perfect state transfer graphs. Moreover, on a hypercube, we show that perfect state transfer occurs between uniform superpositions on pairs of arbitrary subcubes, thus generalizing results of Bernasconi et al.2 and Moore and Russell.3

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16

Markham, Damian, and Alexandra Krause. "A Simple Protocol for Certifying Graph States and Applications in Quantum Networks." Cryptography 4, no. 1 (January 22, 2020): 3. http://dx.doi.org/10.3390/cryptography4010003.

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We present a simple protocol for certifying graph states in quantum networks using stabiliser measurements. The certification statements can easily be applied to different protocols using graph states. We see, for example, how it can be used for measurement based verified quantum computation, certified sampling of random unitaries, quantum metrology and sharing quantum secrets over untrusted channels.

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17

Liao, Longxia, Xiaoqi Peng, Jinjing Shi, and Ying Guo. "Graph State-Based Quantum Group Authentication Scheme." Journal of the Physical Society of Japan 86, no. 2 (February 15, 2017): 024403. http://dx.doi.org/10.7566/jpsj.86.024403.

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18

Tian, Yu-Ling, Tian-Feng Feng, and Xiao-Qi Zhou. "Collaborative quantum computation with redundant graph state." Acta Physica Sinica 68, no. 11 (2019): 110302. http://dx.doi.org/10.7498/aps.68.20190142.

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19

Smaczyński, Marek, Wojciech Roga, and Karol Życzkowski. "Selfcomplementary Quantum Channels." Open Systems & Information Dynamics 23, no. 03 (September 2016): 1650014. http://dx.doi.org/10.1142/s1230161216500141.

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Selfcomplementary quantum channels are characterized by such an interaction between the principal quantum system and the environment that leads to the same output states of both interacting systems. These maps can describe approximate quantum copy machines, as perfect copying of an unknown quantum state is not possible due to the celebrated no-cloning theorem. We provide here a parametrization of a large class of selfcomplementary channels and analyze their properties. Selfcomplementary channels preserve some residual coherences and residual entanglement. Investigating some measures of non-Markovianity, we show that time evolution under selfcomplementary channels is highly non-Markovian.

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20

Iriyama, Satoshi, and Noboru Watanabe. "On Classification of Quantum Channels." Open Systems & Information Dynamics 08, no. 01 (March 2001): 73–88. http://dx.doi.org/10.1023/a:1011365917780.

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Quantum mutual entropy and quantum capacity are rigorously defined by Ohya, and they are quite useful in the study of quantum communication processes [4, 7, 8, 9,10]. Mathematical models of optical communication processes are described by a quantum channel and optical states, and quantum capacity is one of the most important criteria to measure the efficiency of information transmission [4,7,8]. In actual optical communication, a laser beam is used for a signal, and it is denoted mathematically by a coherent state. Further, optical communication using a squeezed state, which is expected to be more efficient than that using a coherent state is proposed. In this paper, we define several quantum channels, that is, a squeezed channel and a coherent channel and so on. We compare them by calculating quantum capacity.

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21

TIAN, XIU-LAO, GUO-FANG SHI, and Yong ZHAO. "QUANTUM CHANNELS OF THE QUTRIT STATE TELEPORTATION." International Journal of Quantum Information 09, no. 03 (April 2011): 893–901. http://dx.doi.org/10.1142/s0219749911007502.

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Qudit quantum system can carry more information than that of qubit, the teleportation of qudit state has significance in quantum information task. We propose a method to teleport a general qutrit state (three-level state) and discuss the necessary and sufficient condition for realizing a successful and perfect teleportation, which is determined by the measurement matrix Tα and the quantum channel parameter matrix (CPM) X. By using this method, we study the channels of two-qutrit state and three-qutrit state teleportation.

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22

Hilaire, Paul, Leonid Vidro, Hagai S. Eisenberg, and Sophia E. Economou. "Near-deterministic hybrid generation of arbitrary photonic graph states using a single quantum emitter and linear optics." Quantum 7 (April 27, 2023): 992. http://dx.doi.org/10.22331/q-2023-04-27-992.

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Since linear-optical two-photon gates are inherently probabilistic, measurement-based implementations are particularly well suited for photonic platforms: a large highly-entangled photonic resource state, called a graph state, is consumed through measurements to perform a computation. The challenge is thus to produce these graph states. Several generation procedures, which use either interacting quantum emitters or efficient spin-photon interface, have been proposed to create these photonic graph states deterministically. Yet, these solutions are still out of reach experimentally since the state-of-the-art is the generation of a linear graph state. Here, we introduce near-deterministic solutions for the generation of graph states using the current quantum emitter capabilities. We propose hybridizing quantum-emitter-based graph state generation with all-photonic fusion gates to produce graph states of complex topology near-deterministically. Our results should pave the way towards the practical implementation of resource-efficient quantum information processing, including measurement-based quantum communication and quantum computing.

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23

Santos, Raqueline A. M. "Quantum state transfer on the complete bipartite graph." Journal of Physics A: Mathematical and Theoretical 55, no. 12 (February 24, 2022): 125301. http://dx.doi.org/10.1088/1751-8121/ac5217.

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Abstract Previously it was shown that (almost) perfect state transfer can be achieved on the complete bipartite graph by a discrete-time coined quantum walk based algorithm when both the sender and receiver vertices are in the same partition of the graph and when the sender and receiver are in opposite partitions of the same size. By changing the coin operator, we analyze the state transfer problem and we show that it is still possible to achieve state transfer with high fidelity even when the sender and receiver are in different partitions with different sizes. Moreover, it is also possible to use an active switch approach using lackadaisical quantum walks where the marked vertex is switched between the sender and receiver during the algorithm.

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24

Wu, Yadong, Runze Cai, Guangqiang He, and Jun Zhang. "Quantum secret sharing with continuous variable graph state." Quantum Information Processing 13, no. 5 (December 17, 2013): 1085–102. http://dx.doi.org/10.1007/s11128-013-0713-7.

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25

Chi, Dong Pyo, and Kabgyun Jeong. "Approximate Quantum State Sharings via Pair of Private Quantum Channels." Journal of Quantum Information Science 04, no. 01 (2014): 64–70. http://dx.doi.org/10.4236/jqis.2014.41006.

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26

Ban, Masashi. "Quantum State Discrimination with Prior Knowledge in Noisy Quantum Channels." International Journal of Theoretical Physics 52, no. 1 (September 15, 2012): 312–21. http://dx.doi.org/10.1007/s10773-012-1335-z.

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27

Herrera-Marti, David A., and Terry Rudolph. "Loss tolerance with a concatenated graph state." Quantum Information and Computation 13, no. 11&12 (November 2013): 995–1006. http://dx.doi.org/10.26421/qic13.11-12-6.

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A new way of addressing loss errors is introduced which combines ideas from measurement-based quantum computation and concatenated quantum codes, allowing for universal quantum computation. It is shown that for the case where qubit loss is detected upon measurement, the scheme performs well under $23\%$ loss rate. For loss rates below $10\%$ this approach performs better than the best scheme known up to date \cite{varnava2006loss}. If lost qubits are tagged prior to measurement, it can tolerate up to $50\%$ loss. The overhead per logical qubit is shown to be significantly lower than other schemes. The obtention of the threshold is entirely analytic.

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Hong, Kyungpyo, and Seungsang Oh. "Enumeration on graph mosaics." Journal of Knot Theory and Its Ramifications 26, no. 05 (April 2017): 1750032. http://dx.doi.org/10.1142/s0218216517500328.

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Since the Jones polynomial was discovered, the connection between knot theory and quantum physics has been of great interest. Lomonaco and Kauffman introduced the knot mosaic system to give a definition of the quantum knot system that is intended to represent an actual physical quantum system. Recently the authors developed an algorithm producing the exact enumeration of knot mosaics, which uses a recursion formula of state matrices. As a sequel to this research program, we similarly define the (embedded) graph mosaic system by using 16 graph mosaic tiles, representing graph diagrams with vertices of valence 3 and 4. We extend the algorithm to produce the exact number of all graph mosaics. The magnified state matrix that is an extension of the state matrix is mainly used.

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29

Lai, Ching-Yi, and Runyao Duan. "On the one-shot zero-error classical capacity of classical-quantum channels assisted by quantum non-signalling correlations." Quantum Information and Computation 17, no. 5&6 (April 2017): 380–98. http://dx.doi.org/10.26421/qic17.5-6-2.

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Duan and Winter studied the one-shot zero-error classical capacity of a quantum channel assisted by quantum non-signalling correlations, and formulated this problem as a semidefinite program depending only on the Kraus operator space of the channel. For the class of classical-quantum channels, they showed that the asymptotic zero-error classical capacity assisted by quantum non-signalling correlations, minimized over all classicalquantum channels with a confusability graph G, is exactly log ϑ(G), where ϑ(G) is the celebrated Lov´asz theta function. In this paper, we show that the one-shot capacity for a classical-quantum channel, induced from a circulant graph G defined by equal-sized cyclotomic cosets, is logbϑ(G)c, which further implies that its asymptotic capacity is log ϑ(G). This type of graphs include the cycle graphs of odd length, the Paley graphs of prime vertices, and the cubit residue graphs of prime vertices. Examples of other graphs are also discussed. This gives Lov´asz ϑ function another operational meaning in zero-error classical-quantum communication.

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HU, KE-XIANG, YAN-WEI WANG, BAI-QI JIN, and YI-ZHUANG ZHENG. "TELEPORTING AN ARBITRARY TWO-PARTICLE STATE VIA W OR W-LIKE STATE." International Journal of Quantum Information 06, no. 05 (October 2008): 1041–49. http://dx.doi.org/10.1142/s0219749908003700.

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In this paper, we present a scheme for quantum teleportation of an arbitrary two-particle state via entangled W state or W-like state channels. We find that the success of teleportation is probabilistic and the corresponding probability only relates to the smaller coefficients of the quantum channels. We further show that the quantum teleportation could achieve higher probability using W-like state as a channel than the W state.

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31

Huo, Meiru, Jiliang Qin, Jialin Cheng, Zhihui Yan, Zhongzhong Qin, Xiaolong Su, Xiaojun Jia, Changde Xie, and Kunchi Peng. "Deterministic quantum teleportation through fiber channels." Science Advances 4, no. 10 (October 2018): eaas9401. http://dx.doi.org/10.1126/sciadv.aas9401.

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Quantum teleportation, which is the transfer of an unknown quantum state from one station to another over a certain distance with the help of nonlocal entanglement shared by a sender and a receiver, has been widely used as a fundamental element in quantum communication and quantum computation. Optical fibers are crucial information channels, but teleportation of continuous variable optical modes through fibers has not been realized so far. Here, we experimentally demonstrate deterministic quantum teleportation of an optical coherent state through fiber channels. Two sub-modes of an Einstein-Podolsky-Rosen entangled state are distributed to a sender and a receiver through a 3.0-km fiber, which acts as a quantum resource. The deterministic teleportation of optical modes over a fiber channel of 6.0 km is realized. A fidelity of 0.62 ± 0.03 is achieved for the retrieved quantum state, which breaks through the classical limit of1/2. Our work provides a feasible scheme to implement deterministic quantum teleportation in communication networks.

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32

Wu, S. J., and X. M. Chen. "Unambiguous unitary quantum channels." Quantum Information and Computation 7, no. 8 (November 2007): 782–98. http://dx.doi.org/10.26421/qic7.8-8.

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Unambiguous unitary maps and unambiguous unitary quantum channels are introduced and some of their properties are derived. These properties ensures certain simple form for the measurements involved in realizing an unambiguous unitary quantum channel. Error correction and unambiguous error correction with nonzero probability are discussed in terms of unambiguous unitary quantum channels. We not only re-derive the well-known condition for a set of errors to be correctable with certainty, but also obtain a necessary and sufficient condition for the errors caused by a noisy channel to be correctable with any nonzero probability. Dense coding with a partially entangled state can also be viewed as an unambiguous unitary quantum channel when all messages are required to be transmitted with equal probability of success, the maximal achievable probability of success is derived and the optimum protocol is also obtained.

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Adcock, Jeremy C., Sam Morley-Short, Axel Dahlberg, and Joshua W. Silverstone. "Mapping graph state orbits under local complementation." Quantum 4 (August 7, 2020): 305. http://dx.doi.org/10.22331/q-2020-08-07-305.

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Graph states, and the entanglement they posses, are central to modern quantum computing and communications architectures. Local complementation – the graph operation that links all local-Clifford equivalent graph states – allows us to classify all stabiliser states by their entanglement. Here, we study the structure of the orbits generated by local complementation, mapping them up to 9 qubits and revealing a rich hidden structure. We provide programs to compute these orbits, along with our data for each of the 587 orbits up to 9 qubits and a means to visualise them. We find direct links between the connectivity of certain orbits with the entanglement properties of their component graph states. Furthermore, we observe the correlations between graph-theoretical orbit properties, such as diameter and colourability, with Schmidt measure and preparation complexity and suggest potential applications. It is well known that graph theory and quantum entanglement have strong interplay – our exploration deepens this relationship, providing new tools with which to probe the nature of entanglement.

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34

Raza, Mohd Arif, Adel N. Alahmadi, Widyan Basaffar, David G. Glynn, Manish K. Gupta, James W. P. Hirschfeld, Abdul Nadim Khan, Hatoon Shoaib, and Patrick Solé. "The Quantum States of a Graph." Mathematics 11, no. 10 (May 16, 2023): 2310. http://dx.doi.org/10.3390/math11102310.

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Quantum codes are crucial building blocks of quantum computers. With a self-dual quantum code is attached, canonically, a unique stabilised quantum state. Improving on a previous publication, we show how to determine the coefficients on the basis of kets in these states. Two important ingredients of the proof are algebraic graph theory and quadratic forms. The Arf invariant, in particular, plays a significant role.

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Gu, Xuemei, Manuel Erhard, Anton Zeilinger, and Mario Krenn. "Quantum experiments and graphs II: Quantum interference, computation, and state generation." Proceedings of the National Academy of Sciences 116, no. 10 (February 15, 2019): 4147–55. http://dx.doi.org/10.1073/pnas.1815884116.

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We present an approach to describe state-of-the-art photonic quantum experiments using graph theory. There, the quantum states are given by the coherent superpositions of perfect matchings. The crucial observation is that introducing complex weights in graphs naturally leads to quantum interference. This viewpoint immediately leads to many interesting results, some of which we present here. First, we identify an experimental unexplored multiphoton interference phenomenon. Second, we find that computing the results of such experiments is #P-hard, which means it is a classically intractable problem dealing with the computation of a matrix function Permanent and its generalization Hafnian. Third, we explain how a recent no-go result applies generally to linear optical quantum experiments, thus revealing important insights into quantum state generation with current photonic technology. Fourth, we show how to describe quantum protocols such as entanglement swapping in a graphical way. The uncovered bridge between quantum experiments and graph theory offers another perspective on a widely used technology and immediately raises many follow-up questions.

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Lovas, Attila, and Attila Andai. "Volume of the space of qubit-qubit channels and state transformations under random quantum channels." Reviews in Mathematical Physics 30, no. 10 (October 12, 2018): 1850019. http://dx.doi.org/10.1142/s0129055x18500198.

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The simplest building blocks for quantum computations are the qubit-qubit quantum channels. In this paper, we analyze the structure of these channels via their Choi representation. The restriction of a quantum channel to the space of classical states (i.e. probability distributions) is called the underlying classical channel. The structure of quantum channels over a fixed classical channel is studied, the volume of the general and unital qubit channels with respect to the Lebesgue measure is computed and explicit formulas are presented for the distribution of the volume of quantum channels over given classical channels. We study the state transformation under uniformly random quantum channels. If one applies a uniformly random quantum channel (general or unital) to a given qubit state, the distribution of the resulted quantum states is presented.

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Ma, Hongling, Fei Li, Ningyi Mao, Yijun Wang, and Ying Guo. "Network-based Arbitrated Quantum Signature Scheme with Graph State." International Journal of Theoretical Physics 56, no. 8 (May 18, 2017): 2551–61. http://dx.doi.org/10.1007/s10773-017-3410-y.

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Adhikari, Satyabrata, Indranil Chakrabarty, and Pankaj Agrawal. "Probabilistic secret sharing through noise quantum channe." Quantum Information and Computation 12, no. 3&4 (March 2012): 253–61. http://dx.doi.org/10.26421/qic12.3-4-5.

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In a realistic situation, the secret sharing of classical or quantum information will involve the transmission of this information through noisy channels. We consider a three qubit pure state. This state becomes a mixed-state when the qubits are distributed over noisy channels. We focus on a specific noisy channel, the phase-damping channel. We propose a protocol for secret sharing of classical information with this and related noisy channels. This protocol can also be thought of as cooperative superdense coding. We also discuss other noisy channels to examine the possibility of secret sharing of classical information.

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Brown, John, Chris Godsil, Devlin Mallory, Abigail Raz, and Christino Tamon. "Perfect state transfer on signed graphs." Quantum Information and Computation 13, no. 5&6 (May 2013): 511–30. http://dx.doi.org/10.26421/qic13.5-6-10.

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We study perfect state transfer of quantum walks on signed graphs. Our aim is to show that negative edges are useful for perfect state transfer. First, we show that the signed join of a negative $2$-clique with any positive $(n,3)$-regular graph has perfect state transfer even if the unsigned join does not. Curiously, the perfect state transfer time improves as $n$ increases. Next, we prove that a signed complete graph has perfect state transfer if its positive subgraph is a regular graph with perfect state transfer and its negative subgraph is periodic. This shows that signing is useful for creating perfect state transfer since no complete graph (except for the $2$-clique) has perfect state transfer. Also, we show that the double-cover of a signed graph has perfect state transfer if the positive subgraph has perfect state transfer and the negative subgraph is periodic.Here, signing is useful for constructing unsigned graphs with perfect state transfer. Finally, we study perfect state transfer on a family of signed graphs called the exterior powers which is derived from a many-fermion quantum walk on graphs.

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Hayden, P., and C. King. "Correcting quantum channels by measuring the environment." Quantum Information and Computation 5, no. 2 (May 2005): 156–60. http://dx.doi.org/10.26421/qic5.2-6.

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We propose an entanglement tensor to quantitatively compute the entanglement of a general pure multipartite quantum state. We compare the ensuing tensor with the concurrence for bipartite state and apply the tensor measure to some interesting examples of entangled three-qubit and four-qubit states. It is shown that in defining the degree of entanglement of a multi-partite state, one needs to make assumptions about the willingness of the parties to cooperate. For such states our tensor becomes a measure of generalized entanglement of assistance. We also discuss the degree of entanglement and the concurrence of assistance of two generic multi-qubit states.

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Shapourian, Hassan, and Alireza Shabani. "Modular architectures to deterministically generate graph states." Quantum 7 (March 2, 2023): 935. http://dx.doi.org/10.22331/q-2023-03-02-935.

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Graph states are a family of stabilizer states which can be tailored towards various applications in photonic quantum computing and quantum communication. In this paper, we present a modular design based on quantum dot emitters coupled to a waveguide and optical fiber delay lines to deterministically generate N-dimensional cluster states and other useful graph states such as tree states and repeater states. Unlike previous proposals, our design requires no two-qubit gates on quantum dots and at most one optical switch, thereby, minimizing challenges usually posed by these requirements. Furthermore, we discuss the error model for our design and demonstrate a fault-tolerant quantum memory with an error threshold of 0.53% in the case of a 3d graph state on a Raussendorf-Harrington-Goyal (RHG) lattice. We also provide a fundamental upper bound on the correctable loss in the fault-tolerant RHG state based on the percolation theory, which is 1.24 dB or 0.24 dB depending on whether the state is directly generated or obtained from a simple cubic cluster state, respectively.

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Kurzyk, Dariusz, Łukasz Pawela, and Zbigniew Puchała. "Relating Entropies of Quantum Channels." Entropy 23, no. 8 (August 10, 2021): 1028. http://dx.doi.org/10.3390/e23081028.

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In this work, we study two different approaches to defining the entropy of a quantum channel. One of these is based on the von Neumann entropy of the corresponding Choi–Jamiołkowski state. The second one is based on the relative entropy of the output of the extended channel relative to the output of the extended completely depolarizing channel. This entropy then needs to be optimized over all possible input states. Our results first show that the former entropy provides an upper bound on the latter. Next, we show that for unital qubit channels, this bound is saturated. Finally, we conjecture and provide numerical intuitions that the bound can also be saturated for random channels as their dimension tends to infinity.

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JIMÉNEZ, OMAR, CARLOS MUÑOZ, ANDREI B. KLIMOV, and ALDO DELGADO. "SHARING OF D-DIMENSIONAL QUANTUM STATES." International Journal of Quantum Information 10, no. 02 (March 2012): 1250003. http://dx.doi.org/10.1142/s0219749912500037.

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We propose a scheme for the deterministic sharing arbitrary qudit states among three distant parties and characterize the set of ideal quantum channels. We also show that the use of non-ideal quantum channels for quantum state sharing can be related to the problem of quantum state discrimination. This allows us to formulate a protocol which leads to perfect quantum state sharing with a finite success probability.

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Wierciński, Tomasz, Mateusz Rock, Robert Zwierzycki, Teresa Zawadzka, and Michał Zawadzki. "Emotion Recognition from Physiological Channels Using Graph Neural Network." Sensors 22, no. 8 (April 13, 2022): 2980. http://dx.doi.org/10.3390/s22082980.

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In recent years, a number of new research papers have emerged on the application of neural networks in affective computing. One of the newest trends observed is the utilization of graph neural networks (GNNs) to recognize emotions. The study presented in the paper follows this trend. Within the work, GraphSleepNet (a GNN for classifying the stages of sleep) was adjusted for emotion recognition and validated for this purpose. The key assumption of the validation was to analyze its correctness for the Circumplex model to further analyze the solution for emotion recognition in the Ekman modal. The novelty of this research is not only the utilization of a GNN network with GraphSleepNet architecture for emotion recognition, but also the analysis of the potential of emotion recognition based on differential entropy features in the Ekman model with a neutral state and a special focus on continuous emotion recognition during the performance of an activity The GNN was validated against the AMIGOS dataset. The research shows how the use of various modalities influences the correctness of the recognition of basic emotions and the neutral state. Moreover, the correctness of the recognition of basic emotions is validated for two configurations of the GNN. The results show numerous interesting observations for Ekman’s model while the accuracy of the Circumplex model is similar to the baseline methods.

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45

CHAMOLI, ARTI, and C. M. BHANDARI. "TELEPORTATION OF UNKNOWN STATE BY QUTRITS." International Journal of Quantum Information 06, no. 02 (April 2008): 369–78. http://dx.doi.org/10.1142/s0219749908003402.

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Quantum entanglement, like other resources, is now considered to be a resource. It can be produced, concentrated if required, swapped, transported and consumed. During recent years, various schemes of quantum state teleportation have been proposed using different types of quantum channels. Not restricting to qubit based systems, qutrit states and channels have also been of considerable interest. In the present paper, we investigate the teleportation of an unknown single qutrit state, as well as a two qutrit state through a three qutrit quantum channel, along with the required operations to recover the state. This is further generalized to the case of teleportation of an n-qutrit system.

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Vempati, Mahathi, Saumya Shah, Nirman Ganguly, and Indranil Chakrabarty. "A-unital Operations and Quantum Conditional Entropy." Quantum 6 (February 2, 2022): 641. http://dx.doi.org/10.22331/q-2022-02-02-641.

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Negative quantum conditional entropy states are key ingredients for information theoretic tasks such as superdense coding, state merging and one-way entanglement distillation. In this work, we ask: how does one detect if a channel is useful in preparing negative conditional entropy states? We answer this question by introducing the class of A-unital channels, which we show are the largest class of conditional entropy non-decreasing channels. We also prove that A-unital channels are precisely the completely free operations for the class of states with non-negative conditional entropy. Furthermore, we study the relationship between A-unital channels and other classes of channels pertinent to the resource theory of entanglement. We then prove similar results for ACVENN: a previously defined, relevant class of states and also relate the maximum and minimum conditional entropy of a state with its von Neumann entropy. The definition of A-unital channels naturally lends itself to a procedure for determining membership of channels in this class. Thus, our work is valuable for the detection of resourceful channels in the context of conditional entropy.

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Idel, Martin, and Robert Konig. "On quantum additive Gaussian noise channels." Quantum Information and Computation 17, no. 3&4 (March 2017): 283–302. http://dx.doi.org/10.26421/qic17.3-4-6.

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We give necessary and sufficient conditions for a Gaussian quantum channel to have a dilation involving a passive, i.e., number-preserving unitary. We then establish a normal form of such channels: any passively dilatable channel is the result of applying passive unitaries to the input and output of a Gaussian additive channel. The latter combine the state of the system with that of the environment by means of a multi-mode beamsplitter.

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ROGA, WOJCIECH, KAROL ŻYCZKOWSKI, and MARK FANNES. "ENTROPIC CHARACTERIZATION OF QUANTUM OPERATIONS." International Journal of Quantum Information 09, no. 04 (June 2011): 1031–45. http://dx.doi.org/10.1142/s0219749911007794.

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We investigate decoherence induced by a quantum channel in terms of minimal output entropy and map entropy. The latter is the von Neumann entropy of the Jamiołkowski state of the channel. Both quantities admit q-Renyi versions. We prove additivity of the map entropy for all q. For the case q = 2, we show that the depolarizing channel has the smallest map entropy among all channels with a given minimal output Renyi entropy of order two. This allows us to characterize pairs of channels such that the output entropy of their tensor product acting on a maximally entangled input state is larger than the sum of the minimal output entropies of the individual channels. We conjecture that for any channel Φ1 acting on a finite dimensional system, there exists a class of channels Φ2 sufficiently close to a unitary map such that additivity of minimal output entropy for Ψ1 ⊗ Ψ2 holds.

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Jung, Eylee, Mi-Ra Hwang, DaeKil Park, Jin-Woo Son, and Sayatnova Tamaryan. "Mixed-state entanglement and quantum teleportation through noisy channels." Journal of Physics A: Mathematical and Theoretical 41, no. 38 (August 22, 2008): 385302. http://dx.doi.org/10.1088/1751-8113/41/38/385302.

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50

Jiang, Min, and Daoyi Dong. "Multi-party quantum state sharing via various probabilistic channels." Quantum Information Processing 12, no. 1 (February 10, 2012): 237–49. http://dx.doi.org/10.1007/s11128-012-0364-0.

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