Efficient numerical method to calculate three-tangle of mixed states

TL;DR

This paper introduces a fast numerical approach using replica exchange Monte Carlo to compute the three-tangle of mixed quantum states, validated against known results and applicable to broader quantum optimization problems.

Contribution

The paper presents a novel numerical method combining an energy function with replica exchange Monte Carlo for calculating three-tangle in mixed states.

Findings

Accurately computes three-tangle for mixed states.

Shows excellent agreement with analytical results.

Applicable to other quantum optimization tasks.

Abstract

We demonstrate an efficient numerical method to calculate three-tangle of general mixed states. We construct a "energy function" (target function) for the three-tangle of the mixed state under certain constrains. The "energy function" (target function) is then optimized via a replica exchange Monte Carlo method. We have extensively tested the method for the examples with known analytical results, showing remarkable agreement. The method can be applied to other optimization problems in quantum information theory.