Quantum correlations and least disturbing local measurements

TL;DR

This paper investigates the quantification of quantum correlations through minimum information loss caused by local measurements in bipartite mixed states, providing explicit formulas and conditions for two-qubit systems.

Contribution

It introduces a general framework for evaluating quantum correlations via minimum information loss and derives explicit solutions for two-qubit states using quadratic and cubic entropies.

Findings

Explicit stationary conditions for minimum information loss.

Closed-form expressions for two-qubit states with quadratic and cubic entropies.

Analysis of maximally mixed marginals, X states, and aligned state mixtures.

Abstract

We examine the evaluation of the minimum information loss due to an unread local measurement in mixed states of bipartite systems, for a general entropic form. Such quantity provides a measure of quantum correlations, reducing for pure states to the generalized entanglement entropy, while in the case of mixed states it vanishes just for classically correlated states with respect to the measured system, as the quantum discord. General stationary conditions are provided, together with their explicit form for general two-qubit states. Closed expressions for the minimum information loss as measured by quadratic and cubic entropies are also derived for general states of two-qubit systems. As application, we analyze the case of states with maximally mixed marginals, where a general evaluation is provided, as well as X states and the mixture of two aligned states.