Emergence of randomness and arrow of time in quantum walks

Shikano, Yutaka; Chisaki, Kota; Segawa, Etsuo; Konno, Norio

doi:10.1103/physreva.81.062129

Cited by 37 publications

(50 citation statements)

References 28 publications

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“…In this section we will consider a succession of unitary evolutions of the QW followed by a process of chirality-andposition measurement [13,14]. Let us take the origin as the initial position of the random walker with the initial condition |Ψ (0)⟩ of Eq.…”

Section: Periodic Measurements In the Chiralitymentioning

confidence: 99%

“…Here the obstacle of decoherence is present owing to imperfections and environmental noise. Several authors have studied the QW subjected to different types of coin operators and sources of decoherence to analyze and verify the principles of quantum theory as well as the passage from the quantum to the classical world [12][13][14][15][16][17]. These works have shown that the decoherence transforms the quantum behavior into a classical diffusive behavior.…”

Section: Introductionmentioning

confidence: 98%

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Quantum walks: Decoherence and coin-flipping games

Romanelli

Hernández

2011

Physica A: Statistical Mechanics and its Applications

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a b s t r a c tWe investigate the global chirality distribution of the quantum walk on the line when decoherence is introduced either through simultaneous measurements of the chirality and particle position, or as a result of broken links. The first mechanism drives the system towards a classical diffusive behavior. This is used to build new quantum games, similar to the spin-flip game. The second mechanism involves two different possibilities: (a) All the quantum walk links have the same probability of being broken. (b) Only the quantum walk links on a half-line are affected by random breakage. In case (a) the decoherence drives the system to a classical Markov process, whose master equation is equivalent to the dynamical equation of the quantum density matrix. This is not the case in (b) where the asymptotic global chirality distribution unexpectedly maintains some dependence with the initial condition. Explicit analytical equations are obtained for all cases.

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Section: Periodic Measurements In the Chiralitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

Quantum walks: Decoherence and coin-flipping games

Romanelli

Hernández

2011

Physica A: Statistical Mechanics and its Applications

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“…A similar model is considered in Ref. [32], where the authors address the randomness induced by the frequent measurements. However, our case is differs fundamentally as we do not reset the coin state after every measurements and we focus on the entropic properties of the system.…”

Section: Discrete Time Quantum Walk As a Source Of Messagesmentioning

confidence: 99%

Entropy rate of message sources driven by quantum walks

Kollár

Koniorczyk

2014

Phys. Rev. A

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The amount of information generated by a discrete time stochastic processes in a single step can be quantified by the entropy rate. We investigate the differences between two discrete time walk models, the discrete time quantum walk and the classical random walk in terms of entropy rate. We develop analytical methods to calculate and approximate it. This allows us to draw conclusions about the differences between classical stochastic and quantum processes in terms of the classical information theory.

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“…Discrete-time quantum walks (DTQWs) [16] offer a versatile platform for the exploration of a wide range of non-trivial geometric and topological phenomena (experiments) [9,17,18] and (theory) [10,[19][20][21][22][23][24][25][26][27][28][29][30]. Furthermore, QWs are robust platforms for modeling a variety of dynamical processes from excitation transfer in spin chains [31,32] to energy transport in biological complexes [33].…”

Section: Discrete-time Quantum Walksmentioning

confidence: 99%

Topology and Holonomy in Discrete-time Quantum Walks

Puentes

2017

Crystals

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We present a research article which formulates the milestones for the understanding and characterization of holonomy and topology of a discrete-time quantum walk architecture, consisting of a unitary step given by a sequence of two non-commuting rotations in parameter space. Unlike other similar systems recently studied in detail in the literature, this system does not present continous 1D topological boundaries, it only presents a discrete number of Dirac points where the quasi-energy gap closes. At these discrete points, the topological winding number is not defined. Therefore, such discrete points represent topological boundaries of dimension zero, and they endow the system with a non-trivial topology. We illustrate the non-trivial character of the system by calculating the Zak phase. We discuss the prospects of this system, we propose a suitable experimental scheme to implement these ideas, and we present preliminary experimental data.

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Emergence of randomness and arrow of time in quantum walks

Cited by 37 publications

References 28 publications

Quantum walks: Decoherence and coin-flipping games

Quantum walks: Decoherence and coin-flipping games

Entropy rate of message sources driven by quantum walks

Topology and Holonomy in Discrete-time Quantum Walks

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