Separability Criterion for Quantum Effects

Ikko Hamamura

Published 2017-09-23Version 1

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 which are used to decide if a given state is entangled have been proposed. In this paper, we propose a separability criteria for quantum effects (binary observables) which can be regarded as a dual version of Bell-CHSH inequality for states. The violation of the dual version of Bell-CHSH inequality was confirmed using IBM's cloud quantum computer. The violation of our inequality rules out the maximal tensor product state space which satisfies information causality and local tomography. As an application, we show that an entangled measurement which violates our inequality is useful for quantum teleportation.