Quantum cryptographic resource distillation and entanglement

TL;DR

This paper explores the relationship between entanglement and cryptographic usefulness in multipartite quantum states, revealing that some bound entangled states can still enable quantum cryptography.

Contribution

It introduces the concept of quantum cryptographic resource distillable rate and demonstrates that certain bound entangled states are useful for cryptography despite being non-distillable.

Findings

Existence of multipartite bound entangled states with positive cryptographic distillable rate

Bound entangled states can be useful for quantum key distribution and secret sharing

Relationship between entanglement properties and cryptographic utility clarified

Abstract

We look into multipartite quantum states on which quantum cryptographic protocols including quantum key distribution and quantum secret sharing can be perfectly performed, and define the quantum cryptographic resource distillable rate as the asymptotic rate at which such multipartite state can be distilled from a given multipartite state. Investigating several relations between entanglement and the rate, we show that there exists a multipartite bound entangled state whose quantum cryptographic resource distillable rate is strictly positive, that is, there exists a multipartite entangled state which is not distillable, but can be useful for quantum cryptography such as quantum key distribution and quantum secret sharing.