Quantum correlations in entangled two-particle non-unitary quantum walks

TL;DR

This paper investigates how quantum correlations evolve in two-particle non-unitary quantum walks with gain and loss, revealing effects of dissipation, symmetry, and topological phases on entanglement and quantum-to-classical transitions.

Contribution

It provides the first detailed analysis of two-particle non-unitary quantum walks, highlighting how dissipation and symmetry affect quantum correlations and topological phase distinctions.

Findings

Entanglement entropy decays slower in antisymmetric states at the exceptional point.

Concurrence on one-particle reduced density remains unaffected by dissipation in antisymmetric states.

Quantum correlations signal quantum-to-classical transition and differentiate topological phases.

Abstract

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.