Chirality asymptotic behavior and non-Markovianity in quantum walks on a line

Hinarejos, M.; Franco, Carlo D.; Romanelli, A.; Perez, A.

doi:10.1103/physreva.89.052330

Cited by 23 publications

(35 citation statements)

References 21 publications

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“…The simplest instance of DTQW is that of a quantum system with two levels translating on a one dimensional discrete position space [29,30], a topology which we use in this work. What makes DTQW especially interesting is that even in the noiseless case, the reduced dynamics of the coin manifests non-Markovian recurrence behavior due to interaction with the position degree of freedom [31]. This could be also envisaged in more complex systems which may possess an inherent non-Markovian feature because of interaction among subsystems.…”

Section: Introductionmentioning

confidence: 99%

Non-Markovian Evolution: a Quantum Walk Perspective

Kumar

Banerjee

Srikanth

et al. 2018

Open Syst. Inf. Dyn.

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Quantum non-Markovianity of a quantum noisy channel is typically identified with information backflow, or, more generally, with departure of the intermediate map from complete positivity. But here, we also indicate certain non-Markovian channels that can't be witnessed by the CP-divisibility criterion. In complex systems, non-Markovianity becomes more involved on account of subsystem dynamics. Here we study various facets of non-Markovian evolution, in the context of coined quantum walks, with particular stress on disambiguating the internal vs. environmental contributions to non-Markovian backflow. For the above problem of disambiguation, we present a general power-spectral technique based on a distinguishability measure such as trace-distance or correlation measure such as mutual information. We also study various facets of quantum correlations in the transition from quantum to classical random walks, under the considered non-Markovian noise models. The potential for the application of this analysis to the quantum statistical dynamics of complex systems is indicated.

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Section: Introductionmentioning

confidence: 99%

Non-Markovian Evolution: a Quantum Walk Perspective

Kumar

Banerjee

Srikanth

et al. 2018

Open Syst. Inf. Dyn.

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“…Considering the obtained expressions P R ( t ) and P L ( t ) for the coin in Eq. 6, when time t approaches infinity, we find that the populations of the coin P R ( t ) and P L ( t ) are affected by the interference term A ( t →∞), We can find that for one dimensional QW, the contribution to the populations of the coin ( P L ( t ) and P R ( t )) is related to the interference term which is associated with the coefficients a x and b x 51 . From the interference terms in Eq.…”

Section: Resultsmentioning

confidence: 83%

Quantum sensing of noises in one and two dimensional quantum walks

Chen

Zhang

2017

Sci Rep

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Quantum walk (QW) provides a versatile platform for the realization of quantum algorithms. Due to the existence of the inevitable noises in the walk, the different quantum algorithms accommodating to different noises are demanded. Thus, the success of the algorithms based on the QW requires us to sense different noises in the walk. Until now, the way to distinguish different noises in the walk has been discussed rarely. Here, we propose an efficient way to sense the noises in the one and two dimensional QWs. The populations of the coin in the walk with or without decoherence are presented. By only detecting the populations of the coin in the QW, we can determine whether there exists the decoherence in the total QW system. Moreover, the non-Markovianity of the coin in the one and two dimensional QWs is revealed, in which the coin is taken as an open quantum system, and the other components of the QW system is taken as the large environment. With the measured value of the non-Markovianity for the coin, we can conjecture which kinds of noise emerges in the one and two dimensional QWs.

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“…Therefore, it is possible that the transition towards equilibrium will show new features. Among these features is the investigation of a non-Markovian behavior previous to the asymptotic regime, as already observed for the QW [39].…”

Section: Entanglementmentioning

confidence: 88%

Quantum walk on a cylinder

et al. 2016

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International audienceWe consider the two-dimensional alternate quantum walk on a cylinder. We concentrate on the study of the motion along the open dimension, in the spirit of looking at the closed coordinate as a small or " hidden " extra dimension. If one starts from localized initial conditions on the lattice, the dynamics of the quantum walk that is obtained after tracing out the small dimension shows the contribution of several components which can be understood from the study of the dispersion relations for this problem. In fact, these components originate from the contribution of the possible values of the quasimomentum in the closed dimension. In the continuous space-time limit, the different components manifest as a set of Dirac equations, with each quasimomentum providing the value of the corresponding mass. We briefly discuss the possible link of these ideas to the simulation of high-energy physical theories that include extra dimensions. Finally, entanglement between the coin and spatial degrees of freedom is studied, showing that the entanglement entropy clearly overcomes the value reached with only one spatial dimension

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Chirality asymptotic behavior and non-Markovianity in quantum walks on a line

Cited by 23 publications

References 21 publications

Non-Markovian Evolution: a Quantum Walk Perspective

Non-Markovian Evolution: a Quantum Walk Perspective

Quantum sensing of noises in one and two dimensional quantum walks

Quantum walk on a cylinder

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