Abstract
We evaluate the degree of quantum correlation between two fermions (bosons) subject to continuous time quantum walks in a one-dimensional ring lattice with periodic boundary conditions. In our approach, no particle-particle interaction is considered. We show that the interference effects due to exchange symmetry can result into the appearance of non-classical correlations. The role played onto the appearance of quantum correlations by the quantum statistics of the particles, the boundary conditions, and the partition of the system is widely investigated. Quantum correlations also been investigated in a model mimicking the ballistic evolution of two indistinguishable particles in a 1D continuous space structure. Our results are consistent with recent quantum optics and electron quantum optics experiments where the showing up of two-particle non-classical correlations has been observed even in the absence of mutual interaction between the particles.
Highlights
Quantum walks (QW) describe the random walk behavior of a quantum particle [1]
EP remains zero for the input state |ψ(23) f(b), while it exhibits oscillations, between 0 and ln 2/2, with a period of π/2 for the other two input states |ψ(12) f(b) and |ψ(13) f(b). While in the former initial configuration the dynamics of the two-particle wavefunction does not result into building up of non-classical correlations, in the latter cases the interference effects are able to produce quantum correlations (QC), whose periodic behavior is strictly related to the evolution of the system in a ring lattice with a small number of nodes with periodic boundary conditions
Such correlations have been related to non trivial interference effects due to the quantum statistics of the particles
Summary
Quantum walks (QW) describe the random walk behavior of a quantum particle [1]. Due to quantum mechanics effects, such as the coherent superposition of wavefunctions and interference, QW exhibit a qualitatively different behavior with respect to classical random walks, such as the ballistic propagation of the wavefunction instead of the diffusive behavior exhibited by the classical probability distribution [2]. Our model does not take into account any kind of particle-particle interaction, so that the time evolution of the two-particle quantum state involving exchange symmetry is essentially ruled by single-particle Hamiltonians describing CTQW In this way, the appearance of QC is only related to two-fermion (-boson) amplitudes interference due to the quantum statistics of the particles involved in the process. In order to estimate the degree of non-classical correlation between the positions of the particles, we adopt the criterion proposed by Wiseman and Vaccaro [16, 18]. Such a criterion, unlike the approach developed by Schliemann [14], behaves correctly under one-site (local) and two-site (non local) transformations.
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