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Non-Markovian decoherent quantum walks

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Chinese Physics B 2013年第7期22卷 56-63页

作者：薛鹏张永生 Department of Physics Southeast University Key Laboratory of quantum Information University of Science and Technology of China

quantum walks act in obviously different ways from their classical counterparts, but decoherence will lessen and close this gap between them. To understand this process, it is necessary to investigate the evolution of quantum walks under different decoherence situations. In this article, we study a non-Markovian decoherent quantum walk on a line. In a short time regime, the behavior of the walk deviates from both ideal quantum walks and classical random walks. The position variance as a measure of the quantum walk collapses and revives for a short time, and tends to have a linear relation with time. That is, the walker’s behavior shows a diffusive spread over a long time limit, which is caused by non-Markovian dephasing affecting the quantum correlations between the quantum walker and his coin. We also study both quantum discord and measurement-induced disturbance as measures of the quantum correlations, and observe both collapse and revival in the short time regime, and the tendency to be zero in the long time limit. Therefore, quantum walks with non-Markovian decoherence tend to have diffusive spreading behavior over long time limits, while in the short time regime they oscillate between ballistic and diffusive spreading behavior, and the quantum correlation collapses and revives due to the memory effect.

关键词： non-Markovian decoherence quantum walks quantum correlations

Disorder in parity-time symmetric quantum walks

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Chinese Physics B 2022年第1期31卷 69-73页

作者： Peng Xue Beijing Computational Science Research Center Beijing 100084China

We experimentally investigate the impact of static disorder and dynamic disorder on the non-unitary dynamics of parity-time(PT)-symmetric quantum *** temporally alternating photon losses in an interferometric network,we realize the passive PT-symmetric quantum dynamics for single *** coin operations allow us to simulate different environmental influences,which result in three different behaviors of quantum walkers:a standard ballistic spread,a diffusive behavior,and a localization,respectively,in a PT-symmetric quantum walk architecture.

关键词： parity-time symmetry quantum walks disorder

The entanglement of deterministic aperiodic quantum walks

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Chinese Physics B 2018年第12期27卷 77-84页

作者： Ting-Ting Liu Ya-Yun Hu Jing Zhao Ming Zhong Pei-Qing Tong Department of Physics and Institute of Theoretical Physics Nanjing Normal UniversityNanjing 210023China physics Department 104Davey LaboratoryPennsylvania State UniversityUniversity ParkPA 16802USA College of Mathematical and Physical Sciences Anshun UniversityAnshun 561000China Laboratory for Numerical Simulation of Large Scale Complex Systems Nanjing Normal UniversityNanjing 210023China

We study the entanglement between the internal(coin)and the external(position)degrees of freedom in the dynamic and the static deterministic aperiodic quantum walks(QWs).For the dynamic(static)aperiodic QWs,the coin depends on the time(position)and takes two coins C(α)and C(β)arranged in the two classes of generalized Fibonacci(GF)and the Thue–Morse(TM)*** found that for the dynamic QWs,the entanglement of three kinds of the aperiodic QWs are close to the maximal value,which are all much larger than that of the homogeneous ***,the first class of GF(1st GF)QWs can achieve the maximum entangled state,which is similar to that of the dynamic disordered *** the entanglement of 1st GF QWs is greater than that of the TM QWs,being followed closely by the entanglement of the second class of GF(2nd GF)*** the static QWs,the entanglement of three kinds of the aperiodic QWs are also close to the maximal value and 1st GF QWs can achieve the maximum entangled *** entanglement of the TM QWs is between1st GF QWs and 2nd GF ***,the entanglement of the static disordered QWs is less than that of three kinds of the aperiodic *** is different from those of the dynamic *** these results,we can conclude that the dynamic and static 1st GF QWs can also be considered as maximal entanglement generators.

关键词： quantum walks quantum entanglement aperiodic entanglement production

A Controlled quantum Dialogue Protocol Based on quantum walks

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Computers, Materials & Continua 2020年第8期64卷 1247-1260页

作者： Jinqiao Dai Shibin Zhang Yan Chang Xueyang Li Tao Zheng Jinyue Xia Chengdu University of Information Technology Chengdu610225China International Business Machines Corporation(IBM) New York10421USA

In order to enable two parties to exchange their secret information equally,we propose a controlled quantum dialogue protocol based on quantum walks,which implements the equal exchange of secret information between the two parties with the help of the controller *** secret information is transmitted via quantum walks,by using this method,the previously required entangled particles do not need to be prepared in the initial phase,and the entangled particles can be produced spontaneously via quantum ***,to resist TP’s dishonest behavior,we use a hash function to verify the correctness of the secret *** protocol analysis shows that it is safe and reliable facing some attacks,including intercept-measure-resend attack,entanglement attack,dishonest controller’s attack and participant *** has a slightly increasing efficiency comparing with the previous *** that the proposed protocol may be feasible because quantum walks prove to be implemented in different physical systems and experiments.

关键词： quantum cryptography controlled quantum dialogue quantum walks quantum teleportation

A two-dimensional quantum walk driven by a single two-side coin

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Chinese Physics B 2020年第11期29卷 92-98页

作者： Quan Lin Hao Qin Kun-Kun Wang Lei Xiao Peng Xue Beijing Computational Science Research Center Beijing 100084China Department of Physics Southeast UniversityNanjing 211189China

We study a two-dimensional quantum walk with only one walker alternatively walking along the horizontal and vertical directions driven by a single two-side *** find the analytical expressions of the first two moments of the walker’s position distribution in the long-time limit,which indicates that the variance of the position distribution grows quadratically with walking steps,showing a ballistic spreading typically for quantum ***,we analyze the correlation by calculating the quantum mutual information and the measurement-induced disturbance respectively as the outcome of the walk in one dimension is correlated to the other with the coin as a *** is shown that the quantum correlation between walker spaces increases gradually with the walking steps.

关键词： quantum walks quantum mutual information measurement-induced disturbance

Implementation of a one-dimensional quantum walk in both position and phase spaces

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Chinese Physics B 2014年第1期23卷 55-59页

作者：秦豪薛鹏 Department of Physics Southeast University State Key Laboratory of Precision Spectroscopy East China Normal University

quantum walks have been investigated as they have remarkably different features in contrast to classical random walks. We present a quantum walk in a one-dimensional architecture, consisting of two coins and a walker whose evolution is in both position and phase spaces alternately controlled by the two coins respectively. By analyzing the dynamics evolution of the walker in both the position and phase spaces, we observe an influence on the quantum walk in one space from that in the other space, which behaves like decoherence. We propose an implementation of the two-coin quantum walk in both position and phase spaces via cavity quantum electrodynamics （QED）.

关键词： quantum walks cavity quantum electrodynamics

A quantum walk in phase space with resonator-assisted double quantum dots

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Chinese Physics B 2016年第2期25卷 93-97页

作者：边志浩秦豪詹翔李剑薛鹏 Department of Physics Southeast University

We implement a quantum walk in phase space with a new mechanism based on the superconducting resonator-assisted double quantum dots. By analyzing the hybrid system, we obtain the necessary factors implementing a quantum walk in phase space： the walker, coin, coin flipping and conditional phase shift. The coin flipping is implemented by adding a driving field to the resonator. The interaction between the quantum dots and resonator is used to implement conditional phase shift. Furthermore, we show that with different driving fields the quantum walk in phase space exhibits a ballistic behavior over 25 steps and numerically analyze the factors influencing the spreading of the walker in phase space.

关键词： quantum walks double quantum dots

quantum cellular automata and free quantum field theory

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Frontiers of physics 2017年第1期12卷 65-75页

作者： Giacomo Mauro D'Ariano Paolo Perinottit QUIT Group Dipartimento di Fisica via Bassi 6 1-27100 Pavia Italy

In a series of recent papers [1-4] it has been shown how free quantum field theory can be derived without using mechanical primitives （including space-time, special relativity, quantization rules, etc.）, but only considering the easiest quantum algorithm encompassing a countable set of quantum systems whose network of interactions satisfies the simple principles of unitarity, homogeneity, locality, and isotropy. This has opened the route to extending the axiomatic information-theoretic derivation of the quantum theory of abstract systems [5, 6] to include quantum field theory. The inherent discrete nature of the informational axiomatization leads to an extension of quantum field theory to a quantum cellular automata theory, where the usual field theory is recovered in a regime where the discrete structure of the automata cannot be probed. A simple heuristic argument sets the scale of discreteness to the Planck scale, and the customary physical regime where discreteness is not visible is the relativistic one of small waveveetors. In this paper we provide a thorough derivation from principles that in the most general case the graph of the quantum cellular automaton is the Cayley graph of a finitely presented group, and showing how for the case corresponding to Euclidean emergent space （where the group resorts to an Abelian one） the automata leads to Weyl, Dirac and Maxwell field dynamics in the relativistic limit. We conclude with some perspectives towards the more general scenario of non-linear automata for interacting quantum field theory.

关键词： quantum automata quantum walks quantum fields axiomatics Planck scale