Simultaneous Detection of High-Dimensional Entanglement for Two Unknown Quantum States

TL;DR

This paper introduces a method to simultaneously detect high-dimensional entanglement in two unknown quantum states using local measurements, providing a practical and more powerful alternative to existing criteria.

Contribution

The authors develop a novel entanglement detection approach based on global and local state overlaps, applicable to two unknown states, and demonstrate its experimental feasibility and superiority over traditional methods.

Findings

The ratio of global to local overlaps bounds the Schmidt number.

The method outperforms purity and fidelity criteria in certain cases.

Efficient local randomized measurements enable practical implementation.

Abstract

The state overlap, quantified via $\tr[\rho \sigma]$, is a metric widely used to assess the closeness between two quantum states $\rho$ and $\sigma$. Although global state overlap alone does not directly capture entanglement properties, we uncover that incorporating local state overlaps provide profound insights into the entanglement characteristics of quantum states. To be precise, the ratio of global to local state overlaps provides a lower bound on the Schmidt number, which is usually used for quantifying high-dimensional entanglement. Unlike conventional methods for detecting entanglement, the approach here can simultaneously reveal entanglement information for two unknown quantum states. Moreover, state overlap can be efficiently determined through local randomized measurement methods, which ensures the experimental feasibility of our approach. In a special case, our criterion reduces to an entanglement criterion that is more powerful than the two criteria used most in experiment--the purity criterion and the fidelity-based criterion and also outperform the $p_3$-PPT method in specific instances. Our findings highlight a promising direction for advancements in entanglement detection experiments.