Discrete-time quantum walks generated by aperiodic fractal sequence of space coin operators

Properties of one-dimensional discrete-time quantum walks (DTQWs) are sensitive to the presence of inhomogeneities in the substrate, which can be generated by defining position-dependent coin operators. Deterministic aperiodic sequences of two or more symbols provide ideal environments where these properties can be explored in a controlled way. Based on an exhaustive numerical study, this work discusses a two-coin model resulting from the construction rules that lead to the usual fractal Cantor set. Although the fraction of the less frequent coin [Formula: see text] as the size of the chain is increased, it leaves peculiar properties in the walker dynamics. They are characterized by the wave function, from which results for the probability distribution and its variance, as well as the entanglement entropy, were obtained. A number of results for different choices of the two coins are presented. The entanglement entropy has shown to be very sensitive to uncovering subtle quantum effects present in the model.

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Discrete-time quantum walks on one-dimensional lattices

The European Physical Journal B ◽

10.1140/epjb/e2010-00267-2 ◽

2010 ◽

Vol 77 (4) ◽

pp. 479-488 ◽

Cited By ~ 9

Author(s):

X.-P. Xu

Keyword(s):

Discrete Time ◽

Quantum Walks ◽

One Dimensional ◽

Time Quantum

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One-dimensional discrete-time quantum walks on random environments

Quantum Information Processing ◽

10.1007/s11128-009-0116-y ◽

2009 ◽

Vol 8 (5) ◽

pp. 387-399 ◽

Cited By ~ 36

Author(s):

Norio Konno

Keyword(s):

Discrete Time ◽

Quantum Walks ◽

Random Environments ◽

One Dimensional ◽

Time Quantum

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A limit theorem for a splitting distribution of a quantum walk

International Journal of Quantum Information ◽

10.1142/s0219749918500235 ◽

2018 ◽

Vol 16 (03) ◽

pp. 1850023

Author(s):

Takuya Machida

Keyword(s):

Limit Theorem ◽

Probability Distribution ◽

Random Walks ◽

Discrete Time ◽

Limit Distribution ◽

Quantum Walk ◽

Quantum Walks ◽

Unitary Evolution ◽

Time Quantum ◽

Long Time

Discrete-time quantum walks are considered a counterpart of random walks and their study has been getting attention since around 2000. In this paper, we focus on a quantum walk which generates a probability distribution splitting to two parts. The quantum walker with two coin states spreads at points, represented by integers, and we analyze the chance of finding the walker at each position after it carries out a unitary evolution a lot of times. The result is reported as a long-time limit distribution from which one can see an approximation to the finding probability.

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The fog on: Generalized teleportation by means of discrete-time quantum walks on N-lines and N-cycles

Modern Physics Letters B ◽

10.1142/s0217984919502701 ◽

2019 ◽

Vol 33 (23) ◽

pp. 1950270 ◽

Cited By ~ 4

Author(s):

Duc Manh Nguyen ◽

Sunghwan Kim

Keyword(s):

Discrete Time ◽

Quantum Teleportation ◽

Quantum Walk ◽

Quantum Walks ◽

One Dimensional ◽

Time Quantum ◽

Infinite Line ◽

The One

The recent paper entitled “Generalized teleportation by means of discrete-time quantum walks on [Formula: see text]-lines and [Formula: see text]-cycles” by Yang et al. [Mod. Phys. Lett. B 33(6) (2019) 1950069] proposed the quantum teleportation by means of discrete-time quantum walks on [Formula: see text]-lines and [Formula: see text]-cycles. However, further investigation shows that the quantum walk over the one-dimensional infinite line can be based over the [Formula: see text]-cycles and cannot be based on [Formula: see text]-lines. The proofs of our claims on quantum walks based on finite lines are also provided in detail.

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