Informational correlation between two parties of a quantum system: short spin-1/2 chains with XY Hamiltonian

TL;DR

This paper introduces a measure of informational correlation between two quantum subsystems, demonstrating how local transformations affect this correlation in spin-1/2 chains with XY Hamiltonian, revealing non-reducible components.

Contribution

It defines the informational correlation $E^{AB}$ and analyzes its properties and dynamics in spin-1/2 chains, highlighting non-reducible parts unaffected by local transformations.

Findings

Informational correlation $E^{AB}$ can be affected by local unitary transformations.

A non-reducible component of $E^{AB}$ exists that cannot be decreased by local transformations.

Examples in four-node spin-1/2 chains illustrate the behavior of informational correlation.

Abstract

We introduce the informational correlation $E^{AB}$ between two interacting quantum subsystems $A$ and $B$ of a quantum system as the number of arbitrary parameters $\varphi_i$ of a unitary transformation $U^A$ (locally performed on the subsystem $A$) which may be detected in the subsystem $B$ by the local measurements. This quantity indicates whether the state of the subsystem $B$ may be effected by means of the unitary transformation applied to the subsystem $A$. Emphasize that $E^{AB}\neq E^{BA}$ in general. The informational correlations in systems with tensor product initial states are studied in more details. In particular, it is shown that the informational correlation may be changed by the local unitary transformations of the subsystem $B$. However, there is some non-reducible part of $E^{AB}(t)$ which may not be decreased by any unitary transformation of the subsystem $B$ at a fixed time instant $t$. Two examples of the informational correlations between two parties of the four node spin-1/2 chain are studied.