TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhysCore.6.3.048
TI  - A simple coin for a 2d entangled walk
PY  - 2023/07/10
UR  - https://scipost.org/SciPostPhysCore.6.3.048
JF  - SciPost Physics Core
JA  - SciPost Phys. Core
VL  - 6
IS  - 3
SP  - 048
A1  - Zahed, Ahmadullah
AU  - Sen, Kallol
AB  - 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.
ER  -

@Article{10.21468/SciPostPhysCore.6.3.048,
	title={{A simple coin for a 2d entangled walk}},
	author={Ahmadullah Zahed and  Kallol Sen},
	journal={SciPost Phys. Core},
	volume={6},
	pages={048},
	year={2023},
	publisher={SciPost},
	doi={10.21468/SciPostPhysCore.6.3.048},
	url={https://scipost.org/10.21468/SciPostPhysCore.6.3.048},
}