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A simple coin for a 2d entangled walk

Zahed, A and Sen, K (2023) A simple coin for a 2d entangled walk. In: SciPost Physics Core, 6 (3).


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Official URL: https://doi.org/10.21468/SciPostPhysCore.6.3.048


We analyze the effect of a simple coin operator, built out of Bell pairs, in a 2d Discrete Quantum Random Walk (DQRW) problem. The specific form of the coin enables us to find analytical and closed form solutions to the recursion relations of the DQRW. The coin induces entanglement between the spin and position degrees of freedom, which oscillates with time and reaches a constant value asymptotically. We probe the entangling properties of the coin operator further, by two different measures. First, by integrating over the space of initial tensor product states, we determine the Entangling Power of the coin operator. Secondly, we compute the Generalized Relative Rényi Entropy between the corresponding density matrices for the entangled state and the initial pure unentangled state. Both the Entangling Power and Generalized Relative Rényi Entropy behaves similar to the entanglement with time. Finally, in the continuum limit, the specific coin operator reduces the 2d DQRW into two 1d massive fermions coupled to synthetic gauge fields, where both the mass term and the gauge fields are built out of the coin parameters. © 2023 Letters in High Energy Physics. All rights reserved.

Item Type: Journal Article
Publication: SciPost Physics Core
Publisher: SciPost Foundation
Additional Information: The copyright for this article belongs to the Authors.
Department/Centre: Division of Physical & Mathematical Sciences > Centre for High Energy Physics
Date Deposited: 06 Nov 2023 05:14
Last Modified: 06 Nov 2023 05:14
URI: https://eprints.iisc.ac.in/id/eprint/83057

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