Quantum cryptographic resource distillation and entanglement

Minjin Choi,Soojoon Lee

doi:10.1038/s41598-021-00547-5

Minjin Choi, Soojoon Lee

Open Access

https://doi.org/10.1038/s41598-021-00547-5

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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.

Highlights

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
It can be seen that a quantum cryptographic resource (QCR) state is considered as a generalized version of the private state or the genuine secret sharing state, but is regarded as a resource unit in a quantum cryptographic theory, while a pure maximally entangled state plays a role of a resource unit in entanglement theory
The QCR state that we here deal with is a multipartite quantum state, and a private state on the parties can be obtained from the state by local quantum operations and classical communication (LOCC) so that perfectly secure key distribution is feasible between the dealer party and any player party of the state

Summary

Introduction

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. It has been known that there exist mixed states, called the private states[3,4,5] or the (genuine) secret sharing states[6,7], which can distill perfectly secure key bits or secret bits for secret sharing just by measurement. We here call such mixed states the quantum cryptographic resource (QCR) states. It does not seem to be true that all entangled states are QCR distillable, because its simplest case is not true, that is, there exists a bipartite bound entangled state with positive secret key distillable r ate[3,5,9]

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