Connecting velocity and entanglement in quantum walks

Abstract

We investigate the relation between transport properties and entanglement between the internal (spin) and external (position) degrees of freedom in one-dimensional discrete time quantum walks. We obtain closed-form expressions for the long-time position variance and asymptotic entanglement of quantum walks whose time evolution is given by any balanced quantum coin, starting from any initial qubit and position states following $\delta$-like (local) and Gaussian distributions. We find out that the knowledge of the limit velocity of the walker together with the polar angle of the initial qubit provide the asymptotic entanglement for local states, while this velocity with the quantum coin phases give it for highly delocalized states.

arXiv comment7 pages, 5 figures, two columns, RevTex4-1

References in corpus (26)

• Concentrating Partial Entanglement by Local Operations
• Quantum random walks - an introductory overview
• A Quantum Random Walk Search Algorithm
• Universal computation by quantum walk
• Quantum walks: a comprehensive review
• Universal quantum computation using the discrete time quantum walk
• Controlling discrete quantum walks: coins and intitial states
• Weak limits for quantum random walks
• Photonic quantum walk in a single beam with twisted light
• Quantum walks and wavepacket dynamics on a lattice with twisted photons
• The quantum to classical transition for random walks
• Faster quantum walk algorithm for the two dimensional spatial search
• Ideal negative measurements in quantum walks disprove theories based on classical trajectories
• Entanglement in coined quantum walks on regular graphs
• Quantum walk on the line: entanglement and non-local initial conditions
• Implementing Quantum Walks Using Orbital Angular Momentum of Classical Light
• Dynamically Disordered Quantum Walk as a Maximal Entanglement Generator
• Entangling Power of Disordered Quantum Walks
• Implementation of one-dimensional quantum walks on spin-orbital angular momentum space of photons
• Distribution of chirality in the quantum walk: Markov process and entanglement
• Tailoring discrete quantum walk dynamics via extended initial conditions: Towards homogeneous probability distributions
• Group Velocity of Discrete-Time Quantum Walks
• Creating cat states in one-dimensional quantum walks using delocalized initial states
• Entanglement dynamics and quasi-periodicity in discrete quantum walks
• Asymptotic entanglement in quantum walks from delocalized initial states
• Trojan Quantum Walks

Cited by in corpus (16)

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• Universal and optimal coin sequences for high entanglement generation in 1D discrete time quantum walks
• Weak disorder enhancing the production of entanglement in quantum walks
• Trojan Quantum Walks
• Optimizing the spatial spread of a quantum walk
• Discrete-time quantum walk dispersion control through long-range correlations
• Limit theorems and localization of three state quantum walks on a line defined by generalized Grover coins
• Localization in Quantum Walks with a Single Lattice Defect: A Comparative Study
• Quantum Corralling
• High-fidelity state transfer via quantum walks from delocalized states
• Decoding Quantum Search Advantage: The Critical Role of State Properties in Random Walks
• Absorption-based qubit estimation in discrete-time quantum walks
• Directionality and quantum backfire in continuous-time quantum walks from delocalized states: Exact results
• Asymptotic reduced density matrix of discrete-time quantum walks
• Continuous-time quantum walks on a defective lattice: Boosting the spreading of delocalized states through Parrondo's strategy
• Robustness and classical proxy of entanglement in variants of quantum walk