Role of Steering Inequality In Quantum Key Distribution Protocol

TL;DR

This paper demonstrates that violations of steering inequalities can be effectively utilized in entanglement-assisted quantum key distribution protocols, expanding the tools beyond Bell inequality violations for secure quantum communication.

Contribution

It introduces a novel QKD protocol leveraging steering inequality violations, including states that are Bell-CHSH local, and characterizes their utility based on error rates and inequality violations.

Findings

Steering inequality violations can be used in QKD protocols.

Local filtering can induce violations in initially non-violating states.

Absolutely Bell-CHSH local states can be employed in secure QKD.

Abstract

Violation of Bell's inequality has been the mainspring for secure key generation in an entanglement assisted Quantum Key Distribution(QKD) protocol. Various contributions have relied on the violation of appropriate Bell inequalities to build an appropriate QKD protocol. Residing between Bell nonlocality and entanglement, there exists a hybrid trait of correlations, namely correlations exhibited through the violation of steering inequalities. However, such correlations have not been put to use in QKD protocols as much as their stronger counterpart, the Bell violations. In the present work, we show that the violations of the CJWR(E.G.Cavalcanti,S.J. Jones,H.M Wiseman and M.D. Reid, Phys.Rev.A 80,032112(2009))steering inequalities can act as key ingredients in an entanglement assisted QKD protocol. We work with arbitrary two qubit entangled states, characterize them in accordance with their utility in such protocols. The characterization is based on the quantum bit error rate and violation of a CJWR inequality. Furthermore, we show that subsequent applications of local filtering operations on initially entangled states exhibiting non violation, lead to violations necessary for the successful implementation of the protocol. An additional vindication of our protocol is provided by the use of absolutely Bell-CHSH local states, states which remain Bell-CHSH local even under global unitary operations.