A simple coin for a 2d entangled walk

Zahed, Ahmadullah; Sen, Kallol

doi:10.21468/scipostphyscore.6.3.048

A simple coin for a 2d entangled walk

Journal Article · Mon Jul 10 04:00:00 EDT 2023 · SciPost Physics Core

DOI:https://doi.org/10.21468/scipostphyscore.6.3.048· OSTI ID:2280591

Zahed, Ahmadullah ^[1]; Sen, Kallol ^[2]

Indian Institute of Science, Bangalore (India); Stony Brook University
International Centre for Theoretical Physics (ICTP), São Paulo, SP (Brazil). South American Institute for Fundamental Research

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.

View Accepted Manuscript (DOE)

Research Organization:: Stony Brook Univ., NY (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: FG02-88ER40388

OSTI ID:: 2280591

Journal Information:: SciPost Physics Core, Journal Name: SciPost Physics Core Journal Issue: 3 Vol. 6; ISSN 2666-9366

Publisher:: SciPost FoundationCopyright Statement

Country of Publication:: United States

Language:: English

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