Phase-space approach to the study of decoherence in quantum walks

Abstract

We analyze the quantum walk on a cycle using discrete Wigner functions as a way to represent the states and the evolution of the walker. The method provides some insight on the nature of the interference effects that make quantum and classical walks different. We also study the behavior of the system when the quantum coin carried by the walker interacts with an environment. We show that for this system quantum coherence is robust for initially delocalized states of the walker. The use of phase-space representation enables us to develop an intuitive description of the nature of the decoherence process in this system.

Published version; contains some more details about the entropy

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• Framed Hilbert space: hanging the quasi-probability pictures of quantum theory
• Qubits in phase space: Wigner function approach to quantum error correction and the mean king problem
• Complementarity and quantum walks
• Decoherence in Quantum Walks on the Hypercube
• Quasiprobability distribution functions for periodic phase-spaces: I. Theoretical Aspects
• Decoherence in one-dimensional Quantum Walk
• Decoherence induced by a chaotic environment: A quantum walker with a complex coin
• Non-Markovian continuous-time quantum walks on lattices with dynamical noise
• Extended Cahill and Glauber formalism for finite dimensional spaces II. Applications in quantum tomography and quantum teleportation
• Wigner function for a particle in an infinite lattice
• Non-Unitary Quantum Walks on Hyper-Cycles
• The Limiting Distribution of Decoherent Quantum Random Walks
• Optical implementability of the two-dimensional Quantum Walk
• Decoherent quantum walks driven by a generic coin operation
• Theoretical formulation of finite-dimensional discrete phase spaces: II. On the uncertainty principle for Schwinger unitary operators
• Quantum Optical Random Walk: Quantization Rules and Quantum Simulation of Asymptotics
• Phase-space measurements, decoherence and classicality
• Harnessing quantumness of states using discrete Wigner functions under (non)-Markovian quantum channels
• Interference in discrete Wigner functions
• Tunneling effects in a one-dimensional quantum walk
• Transfiguration of Quantum Walks on a line
• Phase space patterns of quantum transport on ordered and disordered networks
• Analytical expression for variance of homogeneous-position quantum walk with decoherent position
• Wigner formalism for a particle on an infinite lattice: dynamics and spin
• Limit Theorems for Decoherent Two Dimensional Quantum Walks
• Shannon Entropy and Diffusion Coeffcient in Parity-Time Symmetric Quantum Walks