# Measurement-induced nonlocality in arbitrary dimensions in terms of the inverse approximate joint diagonalization

## TL;DR

This paper introduces a new way to measure nonlocality in quantum states using skew information, providing an efficient algorithm for analytic expressions applicable to arbitrary dimensions.

## Contribution

It redefines measurement-induced nonlocality with skew information, introduces an inverse approximate joint diagonalization algorithm, and offers analytic solutions for various quantum states.

## Key findings

- The new measure has clear operational meaning.
- The algorithm is simple, efficient, and stable.
- Analytic expressions are obtained for many quantum states.

## Abstract

Here we focus on the measurement induced nonlocality and present a redefinition in terms of the skew information subject to a broken observable. It is shown that the obtained quantity possesses an obvious operational meaning, can tackle the noncontractivity of the measurement induced nonlocality and has analytic expressions for many quantum states. Most importantly, an inverse approximate joint diagonalization algorithm, due to its simplicity, high efficiency, stability, and state independence, is presented to provide almost analytic expressions for any quantum state, which can also shed light on other aspects in physics.