Beyond Gisin's Theorem and its Applications: Violation of Local Realism by Two-Party Einstein-Podolsky-Rosen Steering

TL;DR

This paper shows that certain mixed multi-qubit states with mutual EPR steering fully violate local realism, extending Gisin's theorem and enabling more feasible quantum secret sharing protocols with only entangled pairs.

Contribution

It establishes a new criterion linking EPR steering to the violation of local realism in mixed states, extending Gisin's theorem to a broader class of states.

Findings

States with mutual EPR steering violate local realism.

Enhanced Gisin's theorem applies to mixed states with steering.

Enables three-party secret sharing with entangled pairs.

Abstract

We demonstrate here that for a given mixed multi-qubit state if there are at least two observers for whom mutual Einstein-Podolsky-Rosen steering is possible, i.e. each observer is able to steer the other qubits into two different pure states by spontaneous collapses due to von Neumann type measurements on his/her qubit, then nonexistence of local realistic models is fully equivalent to quantum entanglement (this is not so without this condition). This result leads to an enhanced version of Gisin's theorem (originally: all pure entangled states violate local realism). Local realism is violated by all mixed states with the above steering property. The new class of states allows one e.g. to perform three party secret sharing with just pairs of entangled qubits, instead of three qubit entanglements (which are currently available with low fidelity). This significantly increases the feasibility of having high performance versions of such protocols. Finally, we discuss some possible applications.