Generalized Einstein-Podolsky-Rosen Steering Paradox

TL;DR

This paper introduces a generalized EPR steering paradox that reveals a fundamental contradiction between quantum mechanics and classical theories, providing new insights and potential applications in quantum communication.

Contribution

It presents a generalized EPR steering paradox with a specific contradictory equality and demonstrates its testability in N-qubit states, advancing understanding of quantum steering.

Findings

The paradox predicts a specific equality between quantum and classical theories.

Steerability is confirmed in N-qubit states under certain measurement conditions.

The work suggests new avenues for quantum teleportation and key distribution schemes.

Abstract

Quantum paradoxes are essential means to reveal the incompatibility between quantum and classical theories, among which the Einstein-Podolsky-Rosen (EPR) steering paradox offers a sharper criterion for the contradiction between local-hidden-state model and quantum mechanics than the usual inequality-based method. In this work, we present a generalized EPR steering paradox, which predicts a contradictory equality $2_{Q}=\left( 1+\delta\right)_{C}$ ($0\leq\delta<1$) given by the quantum ($Q$) and classical ($C$) theories. For any $N$-qubit state in which the conditional state of the steered party is pure, we test the paradox through a two-setting steering protocol, and find that the state is steerable if some specific measurement requirements are satisfied. Moreover, our construction also enlightens the building of EPR steering inequality, which may contribute to some schemes for typical quantum teleportation and quantum key distributions.