Quantum walks on the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>N</mml:mi></mml:math>-cycle subject to decoherence on the coin degree of freedom

Liu, Chaobin; Petulante, Nelson

doi:10.1103/physreve.81.031113

Cited by 21 publications

(22 citation statements)

References 26 publications

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“…Decoherence in a QW and the transition of a QW to a CRW is quite important from the viewpoint of practical implementation, and it has been studied by various authors [21][22][23][24][25][26][27]. In particular, in Refs.…”

Section: Introductionmentioning

confidence: 99%

Quantumness of noisy quantum walks: A comparison between measurement-induced disturbance and quantum discord

Rao

Srikanth²,

Chandrashekar³

et al. 2011

Phys. Rev. A

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Noisy quantum walks are studied from the perspective of comparing their quantumness as defined by two popular measures, measurement-induced disturbance (MID) and quantum discord (QD). While the former has an operational definition, unlike the latter, it also tends to overestimate nonclassicality because of a lack of optimization over local measurements. Applied to quantum walks, we find that MID, while acting as a loose upper bound on QD, still tends to reflect correctly trends in the behavior of the latter. However, there are regimes where its behavior is not indicative of nonclassicality: in particular, we find an instance where MID increases with the application of noise, where we expect a reduction of quantumness.

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Section: Introductionmentioning

confidence: 99%

Quantumness of noisy quantum walks: A comparison between measurement-induced disturbance and quantum discord

Rao

Srikanth²,

Chandrashekar³

et al. 2011

Phys. Rev. A

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“…When considering the real experimental implementation, the physical system will have an inevitable interaction with the surrounding environment. Many studies of DTQW report that due to the decoherence induced by the environment, the position distribution pattern of QW change to a binomial distribution that is similar to the distribution of the classical walk [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34]. For the coherent QW, the variance of position distribution in the QW grows quadratically with time.…”

Section: Introductionmentioning

confidence: 99%

Extraordinary behaviors in a two-dimensional decoherent alternative quantum walk

Chen

Zhang

2016

Phys. Rev. A

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The quantum and classical behaviors of two-dimensional (2D) alternative quantum walk (AQW) in the presence of decoherence have been discussed in detail. For any kinds of decoherence, the analytic expressions for the moments of position distribution of AQW have been obtained. Taking the broken line noise and coin-decoherence as examples of decoherence, we find that when the decoherence only emerges in one direction, the anisotropic position distribution pattern appears, and not all the motions of quantum walkers exhibit the transition from quantum to classical behaviors. The correlations between the walkers and the coin in 2D AQW have been discussed. The anisotropic correlations between walkers and coin have been revealed in the presence of decoherence.

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“…where Part of the above lemma has been obtained by Liu and Petulante in [9], but our lemma extends the equality part of their lemma to a wider scope with more applications.…”

Section: Qed 4 Applicationsmentioning

confidence: 95%

“…By the proof of Lemma 1 in [9], the equality holds if and only if (2p − p 2 )(ô 2 12 +ô 2 21 ) = 0. That is, p = 0 or o 12 =ô 21 = 0.…”

Section: Qed 4 Applicationsmentioning

confidence: 99%

Convergence of quantum random walks with decoherence

et al. 2011

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In this paper, we study the discrete-time quantum random walks on a line subject to decoherence. The convergence of the rescaled position probability distribution p(x, t) depends mainly on the spectrum of the superoperator L kk . We show that if 1 is an eigenvalue of the superoperator with multiplicity one and there is no other eigenvalue whose modulus equals to 1, thenP ( ν √ t , t) converges to a convex combination of normal distributions. In terms of position space, the rescaled probability mass function p t (x, t) ≡ p( √ tx, t), x ∈ Z/ √ t, converges in distribution to a continuous convex combination of normal distributions. We give an necessary and sufficient condition for a U (2) decoherent quantum walk that satisfies the eigenvalue conditions. We also give a complete description of the behavior of quantum walks whose eigenvalues do not satisfy these assumptions. Specific examples such as the Hadamard walk, walks 1 under real and complex rotations are illustrated. For the O(2) quantum random walks, an explicit formula is provided for the scaling limit of p(x, t) and their moments. We also obtain exact critical exponents for their moments at the critical point and show universality classes with respect to these critical exponents.

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Quantum walks on theN-cycle subject to decoherence on the coin degree of freedom

Cited by 21 publications

References 26 publications

Quantumness of noisy quantum walks: A comparison between measurement-induced disturbance and quantum discord

Quantumness of noisy quantum walks: A comparison between measurement-induced disturbance and quantum discord

Extraordinary behaviors in a two-dimensional decoherent alternative quantum walk

Convergence of quantum random walks with decoherence

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