No-cloning of quantum steering

TL;DR

This paper demonstrates that quantum steering cannot be cloned onto both copies of a maximally-entangled pair, revealing a fundamental restriction that enhances security in quantum communication.

Contribution

It introduces the concept of 'no-cloning of quantum steering' and proves that steering can only be present in one clone, not both, after universal cloning.

Findings

EPR steering is only present in one clone after universal cloning.

The no-cloning of quantum steering applies to both bipartite and single-system scenarios.

This restriction underpins the security of quantum communication protocols against cloning attacks.

Abstract

Einstein-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.