No-cloning of quantum steering

Ching-Yi Chiu,Che-Ming Li,Franco Nori,Teh-Lu Liao,Neill Lambert

doi:10.1038/npjqi.2016.20

Abstract

AbstractEinstein–Podolsky–Rosen (EPR) steering allows two parties to verify their entanglement, even if one party’s measurements are untrusted. This concept has not only provided new insights into the nature of non-local spatial correlations in quantum mechanics, but also serves as a resource for one-sided device-independent quantum information tasks. Here, we investigate how EPR steering behaves when one-half of a maximally entangled pair of qudits (multidimensional quantum systems) is cloned by a universal cloning machine. We find that EPR steering, as verified by a criterion based on the mutual information between qudits, can only be found in one of the copy subsystems but not both. We prove that this is also true for the single-system analogue of EPR steering. We find that this restriction, which we term ‘no-cloning of quantum steering’, elucidates the physical reason why steering can be used to secure sources and channels against cloning-based attacks when implementing quantum communication and quantum computation protocols.

Highlights

Einstein–Podolsky–Rosen (EPR) steering reveals that one party, Alice, can affect, or steer another remote party (Bob’s) state, by her measurements on one particle of an entangled pair shared between them.[1]
We find that EPR steering, as described by a criterion based on the mutual information between two parties, can only be observed in one of the two copy subsystems, but not both
We investigated how quantum steering is cloned by a universal cloning machine and shared between two copy subsystems

Summary

Introduction

Einstein–Podolsky–Rosen (EPR) steering reveals that one party, Alice, can affect, or steer another remote party (Bob’s) state, by her measurements on one particle of an entangled pair shared between them.[1] This concept was originally introduced by Schrödinger in response to the EPR paradox.[2] Recently, it has been reformulated by Wiseman et al.[3] as an information-theoretic task to demonstrate that Alice and Bob can validate shared entanglement even if the measurement devices of Alice are untrusted. Such a universal cloning machine has been shown to be optimal and has been extensively studied in the context of possible alternatives, extensions and use as an eavesdropping attack on the protocols of quantum cryptography.[8]

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Results

Conclusion