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arXiv:2204.07322 · Chinese Physics Letters

Quantum Cloning of Steering

Dian Zhu, Wei-Min Shang, Fulin Zhang, Jing-Ling Chen

Published May 25, 2022• 7 citations
arXivHTMLPDF

Abstract

Quantum steering in a global state allows an observer to remotely steer a subsystem into different ensembles by performing different local measurements on the other part. We show that, in general, this property cannot be perfectly cloned by any joint operation between a steered subsystem and a third system. Perfect cloning is viable if and only if the initial state is of zero discord. We also investigate the process of cloning the steered qubit of a Bell state using a universal cloning machine. Einstein–Podolsky–Rosen (EPR) steering, which is a type of quantum correlation existing in the states without a local-hidden-state model, is observed in the two copy subsystems. This contradicts the conclusion of no-cloning of quantum steering (EPR steering) [C. Y. Chiu et al., npj Quantum Inf. 2, 16020 (2016)] based on a mutual information criterion for EPR steering.

DOI
10.1088/0256-307x/39/7/070302

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Quantum steering in a global state allows an observer to remotely steer a subsystem into different ensembles by performing different local measurements on the other part. We show that, in general, this property cannot be perfectly cloned by any joint operation between a steered subsystem and a third system. Perfect cloning is viable if and only if the initial state is of zero discord. We also investigate the process of cloning the steered qubit of a Bell state using a universal cloning machine. Einstein–Podolsky–Rosen (EPR) steering, which is a type of quantum correlation existing in the states without a local-hidden-state model, is observed in the two copy subsystems. This contradicts the conclusion of no-cloning of quantum steering (EPR steering) [C. Y. Chiu et al., npj Quantum Inf. 2, 16020 (2016)] based on a mutual information criterion for EPR steering.
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.
Einstein-Podolsky-Rosen (EPR) steering is the explicit demonstration of the fact that the measurements of one party can influence the quantum state held by another distant party and do so even if the measurements themselves are untrusted. This has been shown to allow one-sided device-independent quantum information tasks between two remote parties. However, in general, advanced multiparty protocols for generic quantum technologies, such as quantum secret sharing and blind quantum computing for quantum networks, demand multipartite quantum correlations of graph states shared between more than two parties. Here, we show that when one part of a quantum multidimensional system composed of a two-colorable graph state (e.g., cluster and Greenberger-Horne-Zeilinger states) is attacked by an eavesdropper using a universal cloning machine, only one of the copy subsystems can exhibit multipartite EPR steering but not both. Such a no-sharing restriction secures both state sources and channels against cloning-based attacks for generic quantum networking tasks, such as distributed quantum information processing, in the presence of uncharacterized measurement apparatuses.
Einstein-Podolsky-Rosen (EPR) steering, a fundamental concept of quantum nonlocality, describes one observer's capability to remotely affect another distant observer's state by local measurements. Unlike quantum entanglement and Bell nonlocality, both associated with the symmetric quantum correlation, EPR steering depicts the unique asymmetric property of quantum nonlocality. With the local filter operation in which some system components are discarded, quantum nonlocality can be distilled to enhance the nonlocal correlation and even the hidden nonlocality can be activated. However, asymmetric quantum nonlocality in the filter operation still lacks a well-rounded investigation, especially considering the discarded parts where quantum nonlocal correlations may still exist with probabilities. Here, in both theory and experiment, we investigate the effect of reusing the discarded particles from local filter. We observe all configurations of EPR steering simultaneously and other intriguing evolution of asymmetric quantum nonlocality, such as reversing the direction of one-way EPR steering. This work provides a perspective to answer ``what is the essential role of utilizing quantum steering as a resource?'' and demonstrates a practical toolbox for manipulating asymmetric quantum systems with significant potential applications in quantum information tasks.
Einstein-Podolsky-Rosen (EPR) steering describes the ability of one observer to nonlocally "steer" the other observer's state through local measurements. EPR steering exhibits a unique asymmetric property; i.e., the steerability can differ between observers, which can lead to one-way EPR steering in which only one observer obtains steerability in the steering process. This property is inherently different from the symmetric concepts of entanglement and Bell nonlocality, and it has attracted increasing interest. Here, we experimentally demonstrate asymmetric EPR steering for a class of two-qubit states in the case of two measurement settings. We propose a practical method to quantify the steerability. We then provide a necessary and sufficient condition for EPR steering and clearly demonstrate one-way EPR steering. Our work provides new insight into the fundamental asymmetry of quantum nonlocality and has potential applications in asymmetric quantum information processing.
Einstein-Podolsky-Rosen (EPR) steering describes how different ensembles of quantum states can be remotely prepared by measuring one particle of an entangled pair. Here, we investigate quantum steering for single quantum ddd-dimensional systems (qudits) and devise efficient conditions to certify the steerability therein, which we find are applicable both to single-system steering and EPR steering. In the single-system case our steering conditions enable the unambiguous ruling out of generic classical means of mimicking steering. Ruling out ``false-steering'' scenarios has implications for securing channels against both cloning-based individual attack and coherent attacks when implementing quantum key distribution using qudits. We also show that these steering conditions also have applications in quantum computation, in that they can serve as an efficient criterion for the evaluation of quantum logic gates of arbitrary size. Finally, we describe how the nonlocal EPR variant of these conditions also function as tools for identifying faithful one-way quantum computation, secure entanglement-based quantum communication, and genuine multipartite EPR steering.
Einstein-Podolsky-Rosen (EPR) steering, a category of quantum nonlocal correlations describing the ability of one observer to influence another party's state via local measurements, is different from both entanglement and Bell nonlocality by possessing an asymmetric property. For multipartite EPR steering, the monogamous situation, where two observers cannot simultaneously steer the state of the third party, has been investigated rigorously both in theory and experiment. In contrast to the monogamous situation, the shareability of EPR steering in reduced subsystems allows the state of one party to be steered by two or more observers and thus reveals more configurations of multipartite EPR steering. However, the experimental implementation of such a kind of shareability has still been absent until now. Here, in an optical experiment, we provide a proof-of-principle demonstration of the shareability of EPR steering without the constraint of monogamy in a three-qubit system. Moreover, based on the reduced bipartite EPR steering detection results, we verify the genuine three-qubit entanglement results. This work provides a complementary viewpoint for understanding multipartite EPR steering and has potential applications in many quantum information protocols, such as multipartite entanglement detection, quantum cryptography, and the construction of quantum networks.