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arXiv:1908.04987 · Open Physics

The role of coherence on two-particle quantum walks

Li-Hua Lü, Zhu Shan, You‐Quan Li

Published Nov 25, 2015• 1 citation
arXivHTMLPDF

Abstract

Abstract We investigate the dynamical properties of the two-boson quantum walk in systems with different degrees of coherence, and where the effect of the coherence on the two-boson quantum walk can be naturally introduced. A general analytical expression for the two-boson correlation function, for both pure states and mixed states, is given.We propose a possible two-photon quantum-walk scheme with a mixed initial state, and find that the twophoton correlation function and the average distance between two photons can be influenced by the initial photon distribution, the relative phase, or the degree of coherence. The propagation features of our numerical results can be explained by our analytical two-photon correlation function.

DOI
10.1515/phys-2015-0042

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Abstract We investigate the dynamical properties of the two-boson quantum walk in systems with different degrees of coherence, and where the effect of the coherence on the two-boson quantum walk can be naturally introduced. A general analytical expression for the two-boson correlation function, for both pure states and mixed states, is given.We propose a possible two-photon quantum-walk scheme with a mixed initial state, and find that the twophoton correlation function and the average distance between two photons can be influenced by the initial photon distribution, the relative phase, or the degree of coherence. The propagation features of our numerical results can be explained by our analytical two-photon correlation function.
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We introduce the idea of a quantum walk with two particles and study it for the case of a discrete time walk on a line. We consider both separable and maximally entangled initial conditions, and show how the entanglement and the relative phase between the states describing the coin degree of freedom of each particle will influence the evolution of the quantum walk. In particular, these factors will have consequences for the distance between the particles and the probability of finding them at a given point, yielding results that cannot be obtained from a separable initial state, be it pure or mixed. Finally, we review briefly proposals for implementations.
Quantum walks on a line with a single particle possess a classical analogue. Involving more walkers opens up the possibility of studying collective quantum effects, such as many-particle correlations. In this context, entangled initial states and the indistinguishability of the particles play a role. We consider the directional correlations between two particles performing a quantum walk on a line. For non-interacting particles, we find analytic asymptotic expressions and give the limits of directional correlations. We show that by introducing δ-interaction between the particles, one can exceed the limits for non-interacting particles.
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We study the evolution of quantum correlations in two-particle discrete-time non-unitary quantum walks on a line with gain and loss. The two particles are initially prepared in a maximally entangled state and evolve independently. Using numerically exact calculations of position probability densities, average interparticle distance, entanglement entropy, and concurrence, we examine how dissipation and particle-exchange symmetry of the state (symmetric or antisymmetric) influence the resulting correlations. Notably, we find that the entanglement entropy of the antisymmetric state decays slower than that of the symmetric state at the exceptional point of the model. We also show that, in the antisymmetric state, the concurrence measured on the one-particle reduced density operator is unaffected by dissipation. Furthermore, we discuss how these correlations indicate quantum-to-classical transitions through the appearance of Gaussian position probability densities, sub-linear growth of average interparticle distance after a few steps, and decay of the entanglement entropy. On the other hand, the robustness of the qubit entanglement entropy can differentiate the model's topological phases better than in the one-particle quantum walk scenario.