Systems with stationary distribution of quantum correlations: open spin-1/2 chains with XY interaction

TL;DR

This paper demonstrates that in certain open spin-1/2 chains with XY interaction, quantum correlations like entanglement and discord can be made stationary in a virtual particle basis, simplifying their analysis and potential quantum device applications.

Contribution

The authors identify a basis of virtual particles where quantum correlations remain stationary, and construct large clusters with uniform correlations in open spin chains.

Findings

Quantum correlations are stationary in a specific virtual particle basis.

Large clusters with uniform entanglement/discord can be formed.

Stationary correlations depend only on initial state and Hamiltonian.

Abstract

Although quantum correlations in a quantum system are characterized by the evolving quantities (which are entanglement and discord usually), we reveal such basis (i.e. the set of virtual particles) for the representation of the density matrix that the entanglement and/or discord between any two virtual particles in such representation are stationary. In particular, dealing with the nearest neighbor approximation, this system of virtual particles is represented by the $\beta$-fermions of the Jordan-Wigner transformation. Such systems are important in quantum information devices because the evolution of quantum entanglement/discord leads to the problems of realization of quantum operations. The advantage of stationary entanglement/discord is that they are completely defined by the initial density matrix and by the Hamiltonian governing the quantum dynamics in the system under consideration. Moreover, using the special initial condition together with the special system's geometry, we construct large cluster of virtual particles with the same pairwise entanglement/discord. In other words, the measure of quantum correlations is stationary in this system and correlations are uniformly "distributed" among all virtual particles. As examples, we use both homogeneous and non-homogeneous spin-1/2 open chains with XY-interaction although other types of interactions might be also of interest.