Detecting unfaithful entanglement by multiple fidelities

TL;DR

This paper proposes a modified fidelity-based entanglement witness approach that combines multiple fidelities to certify entanglement in unfaithful quantum states, supported by mathematical analysis and an optimization algorithm.

Contribution

It introduces a novel modification to fidelity-based witnesses using multiple fidelities and provides an algorithm to optimize their design for certifying unfaithful entanglement.

Findings

Modified witnesses can certify entanglement in unfaithful states

Mathematical analysis of the structure of combined fidelity witnesses

An algorithm to find optimal witness configurations

Abstract

Certifying entanglement for unknown quantum states experimentally is a fundamental problem in quantum computing and quantum physics. Because of being easy to implement, a most popular approach for this problem in modern quantum experiments is detecting target quantum states with fidelity-based entanglement witnesses. Specifically, if the fidelity between a target state and an entangled pure state exceeds a certain value, the target state can be guaranteed to be entangled. Recently, however, it has been realized that there exist so-called unfaithful quantum states, which can be entangled, but their entanglement cannot be certified by any fidelity-based entanglement witnesses. In this paper, by specific examples we show that if one makes a slight modification to fidelity-based entanglement witnesses by combining multiple fidelities together, it is still possible to certify entanglement for unfaithful quantum states with this popular technique. Particularly, we will analyze the mathematical structure of the modified entanglement witnesses, and propose an algorithm that can search for the optimal designs for them.