Asymptotic entanglement in quantum walks from delocalized initial states

Abstract

We study the entanglement between the internal (spin) and external (position) degrees of freedom of the one-dimensional discrete time quantum walk starting from local and delocalized initial states whose time evolution is driven by Hadamard and Fourier coins. We obtain the dependence of the asymptotic entanglement with the initial dispersion of the state and establish a way to connect the asymptotic entanglement between local and delocalized states. We find out that the delocalization of the state increases the number of initial spin states which achieves maximal entanglement from two states (local) to a continuous set of spin states (delocalized) given by a simple relation between the angles of the initial spin state. We also carry out numerical simulations of the average entanglement along the time to confront with our analytical results.

One column, 15 pages, 6 figures

References in corpus (3)

• Universal computation by quantum walk
• Tailoring discrete quantum walk dynamics via extended initial conditions: Towards homogeneous probability distributions
• Creating cat states in one-dimensional quantum walks using delocalized initial states

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• Initial-state-dependent thermalization in open qubits
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• Quantum Corralling
• High-fidelity state transfer via quantum walks from delocalized states
• Geometric monotones of violations of quantum realism
• History states of one-dimensional quantum walks
• 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