Journal articles: 'Leggett-Garg Inequalities'

1

Emary, Clive, Neill Lambert, and Franco Nori. "Leggett–Garg inequalities." Reports on Progress in Physics 77, no. 1 (December 23, 2013): 016001. http://dx.doi.org/10.1088/0034-4885/77/1/016001.

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Kumari, Swati, and A. K. Pan. "Inequivalent Leggett-Garg inequalities." EPL (Europhysics Letters) 118, no. 5 (June 1, 2017): 50002. http://dx.doi.org/10.1209/0295-5075/118/50002.

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Allen, John-Mark A., Owen J. E. Maroney, and Stefano Gogioso. "A Stronger Theorem Against Macro-realism." Quantum 1 (July 14, 2017): 13. http://dx.doi.org/10.22331/q-2017-07-14-13.

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Macro-realism is the position that certain macroscopic observables must always possess definite values: e.g. the table is in some definite position, even if we do not know what that is precisely. The traditional understanding is that by assuming macro-realism one can derive the Leggett-Garg inequalities, which constrain the possible statistics from certain experiments. Since quantum experiments can violate the Leggett-Garg inequalities, this is taken to rule out the possibility of macro-realism in a quantum universe. However, recent analyses have exposed loopholes in the Leggett-Garg argument, which allow many types of macro-realism to be compatible with quantum theory and hence violation of the Leggett-Garg inequalities. This paper takes a different approach to ruling out macro-realism and the result is a no-go theorem for macro-realism in quantum theory that is stronger than the Leggett-Garg argument. This approach uses the framework of ontological models: an elegant way to reason about foundational issues in quantum theory which has successfully produced many other recent results, such as the PBR theorem.

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Hess, Karl, Hans De Raedt, and Kristel Michielsen. "From Boole to Leggett-Garg: Epistemology of Bell-Type Inequalities." Advances in Mathematical Physics 2016 (2016): 1–7. http://dx.doi.org/10.1155/2016/4623040.

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In 1862, George Boole derived an inequality for variables that represents a demarcation line between possible and impossible experience. This inequality forms an important milestone in the epistemology of probability theory and probability measures. In 1985 Leggett and Garg derived a physics related inequality, mathematically identical to Boole’s, that according to them represents a demarcation between macroscopic realism and quantum mechanics. We show that a wide gulf separates the “sense impressions” and corresponding data, as well as the postulates of macroscopic realism, from the mathematical abstractions that are used to derive the inequality of Leggett and Garg. If the gulf can be bridged, one may indeed derive the said inequality, which is then clearly a demarcation between possible and impossible experience: it cannot be violated and is not violated by quantum theory. This implies that the Leggett-Garg inequality does not mean that the SQUID flux is not there when nobody looks, as Leggett and Garg suggest, but instead that the probability measures may not be what Leggett and Garg have assumed them to be, when no data can be secured that directly relate to them. We show that similar considerations apply to other quantum interpretation-puzzles such as two-slit experiments.

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Kumari, Swati, and A. K. Pan. "Various formulations of inequivalent Leggett–Garg inequalities." Journal of Physics A: Mathematical and Theoretical 54, no. 3 (December 31, 2020): 035301. http://dx.doi.org/10.1088/1751-8121/abd077.

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Łobejko, Marcin, and Jerzy Dajka. "Violation of Leggett—Garg inequalities for quantum-classical hybrids." Journal of Physics: Conference Series 626 (July 3, 2015): 012038. http://dx.doi.org/10.1088/1742-6596/626/1/012038.

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Sun, Yong-Nan, Yang Zou, Rong-Chun Ge, Jian-Shun Tang, and Chuan-Feng Li. "Violation of Leggett—Garg Inequalities in Single Quantum Dots." Chinese Physics Letters 29, no. 12 (December 2012): 120302. http://dx.doi.org/10.1088/0256-307x/29/12/120302.

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8

Naikoo, Javid, Swati Kumari, Subhashish Banerjee, and A. K. Pan. "PT symmetric evolution, coherence and violation of Leggett–Garg inequalities." Journal of Physics A: Mathematical and Theoretical 54, no. 27 (June 11, 2021): 275303. http://dx.doi.org/10.1088/1751-8121/ac0546.

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9

Rastegin, Alexey E. "Formulation of Leggett—Garg Inequalities in Terms of q -Entropies." Communications in Theoretical Physics 62, no. 3 (September 2014): 320–26. http://dx.doi.org/10.1088/0253-6102/62/3/05.

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10

Emary, Clive, Neill Lambert, and Franco Nori. "Corrigendum: Leggett–Garg inequalities (2014 Rep. Prog. Phys. 77 016001)." Reports on Progress in Physics 77, no. 3 (February 19, 2014): 039501. http://dx.doi.org/10.1088/0034-4885/77/3/039501.

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Łobejko, Marcin, and Jerzy Dajka. "Leggett-Garg inequalities violation via the Fermi contact hyperfine interaction." Fortschritte der Physik 65, no. 6-8 (September 13, 2016): 1600041. http://dx.doi.org/10.1002/prop.201600041.

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Kalaga, Joanna K., Anna Kowalewska-Kudłaszyk, Mateusz Nowotarski, and Wiesław Leoński. "Violation of Leggett–Garg Inequalities in a Kerr-Type Chaotic System." Photonics 8, no. 1 (January 15, 2021): 20. http://dx.doi.org/10.3390/photonics8010020.

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We consider a quantum nonlinear Kerr-like oscillator externally pumped by a series of ultrashort coherent pulses to analyze the quantum time-correlations appearing while the system evolves. For that purpose, we examine the violation of the Leggett–Garg inequality. We show how the character of such correlations changes when the system’s dynamics correspond to the regular and chaotic regions of its classical counterpart.

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13

Das, Siddhartha, S. Aravinda, R. Srikanth, and Dipankar Home. "Unification of Bell, Leggett-Garg and Kochen-Specker inequalities: Hybrid spatio-temporal inequalities." EPL (Europhysics Letters) 104, no. 6 (December 1, 2013): 60006. http://dx.doi.org/10.1209/0295-5075/104/60006.

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14

Dajka, Jerzy, Marcin Łobejko, and Jerzy Łuczka. "Leggett–Garg inequalities for a quantum top affected by classical noise." Quantum Information Processing 15, no. 11 (August 1, 2016): 4911–25. http://dx.doi.org/10.1007/s11128-016-1401-1.

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15

Wang, Kunkun, Clive Emary, Xiang Zhan, Zhihao Bian, Jian Li, and Peng Xue. "Enhanced violations of Leggett-Garg inequalities in an experimental three-level system." Optics Express 25, no. 25 (December 4, 2017): 31462. http://dx.doi.org/10.1364/oe.25.031462.

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16

Fields, Chris. "Some Consequences of the Thermodynamic Cost of System Identification." Entropy 20, no. 10 (October 17, 2018): 797. http://dx.doi.org/10.3390/e20100797.

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The concept of a “system” is foundational to physics, but the question of how observers identify systems is seldom addressed. Classical thermodynamics restricts observers to finite, finite-resolution observations with which to identify the systems on which “pointer state” measurements are to be made. It is shown that system identification is at best approximate, even in a finite world, and that violations of the Leggett–Garg and Bell/CHSH (Clauser-Horne-Shimony-Holt) inequalities emerge naturally as requirements for successful system identification.

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17

Suzuki, Yutaro, Masataka Iinuma, and Holger F. Hofmann. "Violation of Leggett–Garg inequalities in quantum measurements with variable resolution and back-action." New Journal of Physics 14, no. 10 (October 16, 2012): 103022. http://dx.doi.org/10.1088/1367-2630/14/10/103022.

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18

Halliwell, J. J. "Necessary and sufficient conditions for macrorealism using two- and three-time Leggett-Garg inequalities." Journal of Physics: Conference Series 1275 (September 2019): 012008. http://dx.doi.org/10.1088/1742-6596/1275/1/012008.

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19

Kumari, Asmita, and A. K. Pan. "Quantum violations of L u¨ ders bound Leggett–Garg inequalities for non-unitary quantum channel." Journal of Physics A: Mathematical and Theoretical 55, no. 13 (March 3, 2022): 135301. http://dx.doi.org/10.1088/1751-8121/ac55ec.

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Abstract Leggett Garg inequalities (LGIs) provides an elegant way for probing the incompatibility between the notion of macrorealism and quantum mechanics. For unitary dynamics the optimal quantum violation of a LGI is constrained by the L u ¨ ders bound. In this paper, we have studied two formulations of LGIs in three-time LG scenario, viz, the standard LGIs and third-order LGIs both for unbiased and biased measurement settings. We show that if system evolves under non-unitary quantum channel between two measurements, the quantum violations of both forms of LGIs exceed their respective L u ¨ ders bounds and can even reach their algebraic maximum in sharp measurement settings. We found that when the measurement is unsharp the quantum violations of both standard and third-order LGIs for non-unitary quantum channel can be obtained for lower value of the unsharpness parameter compared to the unitary dynamics. We critically examined the violation of L u ¨ ders bound of LGIs and its relation to the violation of various no-signaling in time conditions, another formalism for testing macrorealism. It is shown that mere violations of no-signaling conditions are not enough to warrant the violation of standard LGIs, an interplay between the violations of various NSIT condition along with a threshold value play an important role. On the other hand violation of third-order LGI is obtained when the degree of violation of a specific no-signaling in time condition reaches a different threshold value.

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20

Yearsley, James M., and Emmanuel M. Pothos. "Challenging the classical notion of time in cognition: a quantum perspective." Proceedings of the Royal Society B: Biological Sciences 281, no. 1781 (April 22, 2014): 20133056. http://dx.doi.org/10.1098/rspb.2013.3056.

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All mental representations change with time. A baseline intuition is that mental representations have specific values at different time points, which may be more or less accessible, depending on noise, forgetting processes, etc. We present a radical alternative, motivated by recent research using the mathematics from quantum theory for cognitive modelling. Such cognitive models raise the possibility that certain possibilities or events may be incompatible, so that perfect knowledge of one necessitates uncertainty for the others. In the context of time-dependence, in physics, this issue is explored with the so-called temporal Bell (TB) or Leggett–Garg inequalities. We consider in detail the theoretical and empirical challenges involved in exploring the TB inequalities in the context of cognitive systems. One interesting conclusion is that we believe the study of the TB inequalities to be empirically more constrained in psychology than in physics. Specifically, we show how the TB inequalities, as applied to cognitive systems, can be derived from two simple assumptions: cognitive realism and cognitive completeness. We discuss possible implications of putative violations of the TB inequalities for cognitive models and our understanding of time in cognition in general. Overall, this paper provides a surprising, novel direction in relation to how time should be conceptualized in cognition.

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21

Hofer, Patrick P. "Quasi-probability distributions for observables in dynamic systems." Quantum 1 (October 12, 2017): 32. http://dx.doi.org/10.22331/q-2017-10-12-32.

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We develop a general framework to investigate fluctuations of non-commuting observables. To this end, we consider the Keldysh quasi-probability distribution (KQPD). This distribution provides a measurement-independent description of the observables of interest and their time-evolution. Nevertheless, positive probability distributions for measurement outcomes can be obtained from the KQPD by taking into account the effect of measurement back-action and imprecision. Negativity in the KQPD can be linked to an interference effect and acts as an indicator for non-classical behavior. Notable examples of the KQPD are the Wigner function and the full counting statistics, both of which have been used extensively to describe systems in the absence as well as in the presence of a measurement apparatus. Here we discuss the KQPD and its moments in detail and connect it to various time-dependent problems including weak values, fluctuating work, and Leggett-Garg inequalities. Our results are illustrated using the simple example of two subsequent, non-commuting spin measurements.

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22

Barbieri, Marco. "Multiple-measurement Leggett-Garg inequalities." Physical Review A 80, no. 3 (September 18, 2009). http://dx.doi.org/10.1103/physreva.80.034102.

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23

Devi, A. R. Usha, H. S. Karthik, Sudha, and A. K. Rajagopal. "Macrorealism from entropic Leggett-Garg inequalities." Physical Review A 87, no. 5 (May 2, 2013). http://dx.doi.org/10.1103/physreva.87.052103.

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24

Martin, Jérôme, and Vincent Vennin. "Leggett-Garg inequalities for squeezed states." Physical Review A 94, no. 5 (November 28, 2016). http://dx.doi.org/10.1103/physreva.94.052135.

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25

"Leggett-Garg Inequalities for Quantum Fluctuating Work." Entropy 20, no. 3 (March 16, 2018): 200. http://dx.doi.org/10.3390/e20030200.

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The Leggett-Garg inequalities serve to test whether or not quantum correlations in time can be explained within a classical macrorealistic framework. We apply this test to thermodynamics and derive a set of Leggett-Garg inequalities for the statistics of fluctuating work done on a quantum system unitarily driven in time. It is shown that these inequalities can be violated in a driven two-level system, thereby demonstrating that there exists no general macrorealistic description of quantum work. These violations are shown to emerge within the standard Two-Projective-Measurement scheme as well as for alternative definitions of fluctuating work that are based on weak measurement. Our results elucidate the influences of temporal correlations on work extraction in the quantum regime and highlight a key difference between quantum and classical thermodynamics.

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26

Chevalier, Hadrien, A. J. Paige, Hyukjoon Kwon, and M. S. Kim. "Violating the Leggett-Garg inequalities with classical light." Physical Review A 103, no. 4 (April 9, 2021). http://dx.doi.org/10.1103/physreva.103.043707.

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27

Matsumura, Akira, Yasusada Nambu, and Kazuhiro Yamamoto. "Leggett-Garg inequalities for testing quantumness of gravity." Physical Review A 106, no. 1 (July 20, 2022). http://dx.doi.org/10.1103/physreva.106.012214.

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28

Giacosa, Francesco, and Giuseppe Pagliara. "Leggett-Garg inequalities and decays of unstable systems." Physical Review A 104, no. 5 (November 29, 2021). http://dx.doi.org/10.1103/physreva.104.052225.

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29

Sokolovski, D., and S. A. Gurvitz. "Paths, negative “probabilities”, and the Leggett-Garg inequalities." Scientific Reports 9, no. 1 (May 8, 2019). http://dx.doi.org/10.1038/s41598-019-43528-5.

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30

Dressel, Justin, and Alexander N. Korotkov. "Avoiding loopholes with hybrid Bell-Leggett-Garg inequalities." Physical Review A 89, no. 1 (January 24, 2014). http://dx.doi.org/10.1103/physreva.89.012125.

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31

Kofler, Johannes, and Časlav Brukner. "Condition for macroscopic realism beyond the Leggett-Garg inequalities." Physical Review A 87, no. 5 (May 13, 2013). http://dx.doi.org/10.1103/physreva.87.052115.

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32

Emary, Clive. "Ambiguous measurements, signaling, and violations of Leggett-Garg inequalities." Physical Review A 96, no. 4 (October 4, 2017). http://dx.doi.org/10.1103/physreva.96.042102.

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33

Emary, Clive. "Leggett-Garg inequalities for the statistics of electron transport." Physical Review B 86, no. 8 (August 9, 2012). http://dx.doi.org/10.1103/physrevb.86.085418.

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34

Santini, Alessandro, and Vittorio Vitale. "Experimental violations of Leggett-Garg inequalities on a quantum computer." Physical Review A 105, no. 3 (March 24, 2022). http://dx.doi.org/10.1103/physreva.105.032610.

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35

Budroni, Costantino, and Clive Emary. "Temporal Quantum Correlations and Leggett-Garg Inequalities in Multilevel Systems." Physical Review Letters 113, no. 5 (July 29, 2014). http://dx.doi.org/10.1103/physrevlett.113.050401.

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36

Avis, David, Patrick Hayden, and Mark M. Wilde. "Leggett-Garg inequalities and the geometry of the cut polytope." Physical Review A 82, no. 3 (September 23, 2010). http://dx.doi.org/10.1103/physreva.82.030102.

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37

Millington, Peter, Zong-Gang Mou, Paul M. Saffin, and Anders Tranberg. "Statistics on Lefschetz thimbles: Bell/Leggett-Garg inequalities and the classical-statistical approximation." Journal of High Energy Physics 2021, no. 3 (March 2021). http://dx.doi.org/10.1007/jhep03(2021)077.

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Abstract Inspired by Lefschetz thimble theory, we treat Quantum Field Theory as a statistical theory with a complex Probability Distribution Function (PDF). Such complex-valued PDFs permit the violation of Bell-type inequalities, which cannot be violated by a real-valued, non-negative PDF. In this paper, we consider the Classical-Statistical approximation in the context of Bell-type inequalities, viz. the familiar (spatial) Bell inequalities and the temporal Leggett-Garg inequalities. We show that the Classical-Statistical approximation does not violate temporal Bell-type inequalities, even though it is in some sense exact for a free theory, whereas the full quantum theory does. We explain the origin of this discrepancy, and point out the key difference between the spatial and temporal Bell-type inequalities. We comment on the import of this work for applications of the Classical-Statistical approximation.

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38

Halliwell, J. J. "Leggett-Garg inequalities and no-signaling in time: A quasiprobability approach." Physical Review A 93, no. 2 (February 26, 2016). http://dx.doi.org/10.1103/physreva.93.022123.

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39

Dressel, J., C. J. Broadbent, J. C. Howell, and A. N. Jordan. "Experimental Violation of Two-Party Leggett-Garg Inequalities with Semiweak Measurements." Physical Review Letters 106, no. 4 (January 24, 2011). http://dx.doi.org/10.1103/physrevlett.106.040402.

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40

Majidy, Shayan, Jonathan J. Halliwell, and Raymond Laflamme. "Detecting violations of macrorealism when the original Leggett-Garg inequalities are satisfied." Physical Review A 103, no. 6 (June 8, 2021). http://dx.doi.org/10.1103/physreva.103.062212.

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41

Halliwell, J. J. "Decoherent histories and measurement of temporal correlation functions for Leggett-Garg inequalities." Physical Review A 94, no. 5 (November 28, 2016). http://dx.doi.org/10.1103/physreva.94.052131.

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42

Halliwell, J. J. "Comparing conditions for macrorealism: Leggett-Garg inequalities versus no-signaling in time." Physical Review A 96, no. 1 (July 20, 2017). http://dx.doi.org/10.1103/physreva.96.012121.

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43

Mendoza-Arenas, J. J., F. J. Gómez-Ruiz, F. J. Rodríguez, and L. Quiroga. "Enhancing violations of Leggett-Garg inequalities in nonequilibrium correlated many-body systems by interactions and decoherence." Scientific Reports 9, no. 1 (November 28, 2019). http://dx.doi.org/10.1038/s41598-019-54121-1.

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AbstractWe identify different schemes to enhance the violation of Leggett-Garg inequalities in open many-body systems. Considering a nonequilibrium archetypical setup of quantum transport, we show that particle interactions control the direction and amplitude of maximal violation, and that in the strongly-interacting and strongly-driven regime bulk dephasing enhances the violation. Through an analytical study of a minimal model we unravel the basic ingredients to explain this decoherence-enhanced quantumness, illustrating that such an effect emerges in a wide variety of systems.

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44

Karthik, H. S., H. Akshata Shenoy, and A. R. Usha Devi. "Leggett-Garg inequalities and temporal correlations for a qubit under PT -symmetric dynamics." Physical Review A 103, no. 3 (March 17, 2021). http://dx.doi.org/10.1103/physreva.103.032420.

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45

Zhang, Kun, Wei Wu, and Jin Wang. "Influence of equilibrium and nonequilibrium environments on macroscopic realism through the Leggett-Garg inequalities." Physical Review A 101, no. 5 (May 22, 2020). http://dx.doi.org/10.1103/physreva.101.052334.

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46

Zhou, Zong-Quan, Susana F. Huelga, Chuan-Feng Li, and Guang-Can Guo. "Experimental Detection of Quantum Coherent Evolution through the Violation of Leggett-Garg-Type Inequalities." Physical Review Letters 115, no. 11 (September 9, 2015). http://dx.doi.org/10.1103/physrevlett.115.113002.

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47

Kumari, Asmita, and A. K. Pan. "Lüders Bounds of Leggett–Garg Inequalities, PT$\mathcal {PT}$‐ Symmetric Evolution and Arrow‐of‐Time." Annalen der Physik, March 2022, 2100401. http://dx.doi.org/10.1002/andp.202100401.

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48

Wang, Kunkun, Mengyan Xu, Lei Xiao, and Peng Xue. "Experimental violations of Leggett-Garg inequalities up to the algebraic maximum for a photonic qubit." Physical Review A 102, no. 2 (August 17, 2020). http://dx.doi.org/10.1103/physreva.102.022214.

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49

Azuma, Hiroo, and Masashi Ban. "The Leggett–Garg inequalities and the relative entropy of coherence in the Bixon–Jortner model." European Physical Journal D 72, no. 10 (October 2018). http://dx.doi.org/10.1140/epjd/e2018-90275-7.

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50

Halliwell, J. J., H. Beck, B. K. B. Lee, and S. O'Brien. "Quasiprobability for the arrival-time problem with links to backflow and the Leggett-Garg inequalities." Physical Review A 99, no. 1 (January 30, 2019). http://dx.doi.org/10.1103/physreva.99.012124.

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Journal articles on the topic 'Leggett-Garg Inequalities'

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