Academic literature on the topic 'Quantum channels on a graph state'

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.

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.

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.

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.

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.

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.

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.

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.