Decoherence on a two-dimensional quantum walk using four- and two-state particle

Abstract

We study the decoherence effects originating from state flipping and depolarization for two-dimensional discrete-time quantum walks using four-state and two-state particles. By quantifying the quantum correlations between the particle and position degree of freedom and between the two spatial ($x-y$) degrees of freedom using measurement induced disturbance (MID), we show that the two schemes using a two-state particle are more robust against decoherence than the Grover walk, which uses a four-state particle. We also show that the symmetries which hold for two-state quantum walks breakdown for the Grover walk, adding to the various other advantages of using two-state particles over four-state particles.

12 pages, 16 figures, In Press, J. Phys. A: Math. Theor. (2013)

References in corpus (39)

• Introducing Quantum Discord
• Quantum random walks - an introductory overview
• Quantum Computation and Decision Trees
• Environment-Assisted Quantum Walks in Photosynthetic Energy Transfer
• Quantum walks of correlated particles
• Quantum Walk in Position Space with Single Optically Trapped Atoms
• Photons Walking the Line: A quantum walk with adjustable coin operations
• Two-particle bosonic-fermionic quantum walk via 3D integrated photonics
• Exploring Topological Phases With Quantum Walks
• From quantum cellular automata to quantum lattice gases
• Realization of quantum walks with negligible decoherence in waveguide lattices
• Realization of a quantum walk with one and two trapped ions
• Quantum walk of a trapped ion in phase space
• Discrete single-photon quantum walks with tunable decoherence
• Decoherence and disorder in quantum walks: From ballistic spread to localization
• Experimental Implementation of Discrete Time Quantum Random Walk on an NMR Quantum Information Processor
• Controlling discrete quantum walks: coins and intitial states
• Quantum walks in higher dimensions
• Experimental Implementation of the Quantum Random-Walk Algorithm
• Decoherence in quantum walks - a review
• Convex-roof extended negativity as an entanglement measure for bipartite quantum systems
• Localization of Two-Dimensional Quantum Walks
• Optimizing the discrete time quantum walk using a SU(2) coin
• Relationship Between Quantum Walk and Relativistic Quantum Mechanics
• Mimicking the probability distribution of a two-dimensional Grover walk with a single-qubit coin
• Recurrence properties of unbiased coined quantum walks on infinite $d$-dimensional lattices
• One- and two-dimensional quantum walks in arrays of optical traps
• Symmetries and noise in quantum walk
• Disordered quantum walk-induced localization of a Bose-Einstein condensate
• Implementing the one-dimensional quantum (Hadamard) walk using a Bose-Einstein Condensate
• Quantum phase transition using quantum walks in an optical lattice
• Alternate two-dimensional quantum walk with a single-qubit coin
• Quantumness of noisy quantum walks: a comparison between measurement-induced disturbance and quantum discord
• Quantumness in decoherent quantum walk using measurement-induced disturbance
• Symmetry-noise interplay in quantum walk on an n-cycle
• Spatial entanglement using a quantum walk on a many-body system
• Quantum Walk with a four-dimensional coin
• Decoherence in Two-Dimensional Quantum Random Walks with Traps
• Distribution and dynamics of entanglement in high-dimensional quantum systems using convex-roof extended negativity

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