Separability Criterion for Quantum Effects

TL;DR

This paper introduces a new separability criterion for quantum effects, specifically binary observables, extending entanglement concepts and demonstrating its violation with quantum computers, impacting quantum information protocols.

Contribution

It proposes a novel separability criterion for quantum effects, dual to the Bell-CHSH inequality, and validates it experimentally using cloud quantum computing.

Findings

Violation of the inequality rules out maximal tensor product state space.

Entangled observables violating the inequality are useful for quantum teleportation.

The criterion provides a new tool for analyzing quantum effects and their role in quantum information.

Abstract

Entanglement of quantum states is absolutely essential for modern quantum sciences and technologies. It is natural to extend the notion of entanglement to quantum observables dual to quantum states. For quantum states, various separability criteria have been proposed to determine whether a given state is entangled. In this Letter, we propose a separability criterion for specific quantum effects (binary observables) that can be regarded as a dual version of the Bell-Clauser-Horne-Shimony-Holt (Bell-CHSH) inequality for quantum states. The violation of the dual version of the Bell-CHSH inequality is confirmed by using IBM's cloud quantum computer. As a consequence, the violation of our inequality rules out the maximal tensor product state space, that satisfies information causality and local tomography. As an application, we show that an entangled observable which violates our inequality is useful for quantum teleportation.