Wigner-Yanase skew information and entanglement generation in quantum measurement

TL;DR

This paper investigates how entanglement generated during quantum premeasurement can be quantified using Wigner-Yanase skew information and the initial state's mixedness, linking quantum correlations to measurement properties.

Contribution

It establishes a quantitative relationship between entanglement, skew information, and mixedness in the premeasurement process for two-level quantum systems.

Findings

Entanglement in premeasurement is quantified by skew information and mixedness.

Negativity of entanglement depends on non-commuting observables.

Skew information measures information about observables not conserved.

Abstract

The first step of quantum measurement procedure is known as \emph{premeasurement}, during when correlation between measuring system and measurement apparatus is established. One compelling non-classical correlation is entanglement, a useful resource for various quantum information theoretic protocols. Quantifying the amount of entanglement in the premeasurement state, therefore, seeks importance from practical ground and this is the central issue of the present paper. Interestingly, for a two-label quantum system we obtain that the amount of entanglement, measured in term of \emph{negativity}, generated in premeasurement process is actually quantified by two factors: \emph{skew information} between system's initial state and the measurement direction, which quantifies the amount of information on the values of observables not commuting with the conserved quantity of the system, and \emph{mixedness parameter} of the system's initial state.