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Physical Review A

Self-testing of genuine multipartite entangled states without network assistance

Ranendu Adhikary, Abhishek Mishra, Ramij Rahaman

Published Jul 3, 2024• 6 citations
Publisher

Abstract

Self-testing of quantum correlations is an important problem in quantum information theory, and the task becomes more challenging in multipartite scenarios. In this context, the authors provide a network-assistance-free self-testing scheme for genuine multipartite entangled states by employing a generalized Hardy-type nonlocality argument and exploring its device-independent bound of the maximum probability of success.

DOI
10.1103/physreva.110.l010401

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Self-testing of quantum correlations is an important problem in quantum information theory, and the task becomes more challenging in multipartite scenarios. In this context, the authors provide a network-assistance-free self-testing scheme for genuine multipartite entangled states by employing a generalized Hardy-type nonlocality argument and exploring its device-independent bound of the maximum probability of success.
Self-testing is a method to certify quantum states and measurements in a device-independent way. The device-independent certification of quantum properties is purely based on input-output measurement statistics of the involved devices with minimal knowledge about their internal workings. Bipartite pure entangled states can be self-tested, but, in the case of multipartite pure entangled states, the answer is not so straightforward. Nevertheless, Šupić et al. recently introduced a novel self-testing method for any pure entangled quantum state, which leverages network assistance and relies on bipartite entangled measurements. Hence, their scheme loses the true device-independent flavor of self-testing. In this regard, we provide a self-testing scheme for genuine multipartite pure entangle states in the true sense by employing a generalized Hardy-type non-local argument. Our scheme involves only local operations and classical communications and does not depend on bipartite entangled measurements and is free from any network assistance. In addition, we provide the device-independent bound of the maximum probability of success for generalized Hardy-type nonlocality argument.
We demonstrate that, in the tripartite scenario with all parties' local events being space-like separated, Hardy-type nonlocality reveals a stronger nonlocal correlation than those captured by Mermin-type inequalities, an important distinction previously unrecognized. To substantiate this assertion, we develop a general framework for tripartite correlations by extending the notion of Settings Independence and Outcome Independence beyond their bipartite formulation. This framework highlights the pivotal role of Hardy-type reasoning in detecting genuine multipartite nonlocality. Furthermore, we show that the tripartite Hardy-nonlocality enables self-testing of a broad class of pure nonmaximally genuine entangled tripartite states, offering a key advantage over Bell inequality-based methods by allowing certification even under nonmaximal violations. Unlike Bell functionals, which typically self-test only a single extremal point, the Hardy relation self-tests a set of extremal correlations for any nonzero Hardy probability. This, in turn, facilitates the device-independent certification of randomness from Hardy-type correlations. We find that the maximum certifiable randomness is ${log}_{2}7\ensuremath{\approx}2.8073$-bits, highlighting both the practical and foundational significance of Hardy-based techniques for quantum randomness generation.
Genuine multipartite nonlocality is a salient feature of quantum systems, empowering the security of multi-party device independent cryptographic protocols. Given a correlation, characterizing and detecting genuineness have been subjected to recent studies. In this regard, we propose a Hardy-type argument which is able to detect genuine nnn-way nonlocality of arbitrary quantum systems. To understand the strength of this argument we also study the optimal success probability of the argument in a minimally constrained theory, namely the generalized no-signaling theory.
Genuine multipartite nonlocality constitutes the strongest form of nonlocality, which is a key resource for many quantum communication and computational tasks. Standard methods for certifying nonlocality often require accessing contradictions in paradoxes or violations of Bell inequalities for composite quantum systems. However, the existing approaches become infeasible and cannot be adopted straightforwardly for a quantum network scenario, which usually possesses complex topological structure and many independent quantum sources. We have developed a simple and customizable strategy to achieve scalable, efficient, and flexible characterizations for various typical quantum network scenarios. The subtle something-versus-nothing contradiction in Hardy-type paradoxes without inequality allows us to substantiate genuine multipartite nonlocality in general quantum networks. Examples range from chain-type network to star-type network, with source connections of any pure entangled permutation symmetric multiqubit states, entangled two-qubit states, etc. The tools extend significantly our ability to certify genuine multipartite nonlocality in state-of-the-art network situations, and make a prominent step forward toward deeper understanding and practical depiction of quantum networks.
Self-testing is an examination for characterizing unknown quantum devices based on correlations of observed statistics in a black-box scenario. With development of large-scale quantum networks, the requirement for self-testing multipartite entangled measurements has become very demanding. We develop here a general procedure for self-testing arbitrary generalized Greenberger-Horne-Zeilinger-state (GHZ-state) measurements which applies to any number of parties. Moreover, it turns out that the existing result for the three-qubit GHZ-state measurement is recovered as a special case. Our results will motivate operational certification of quantum devices related to device-independent quantum information tasks for various scenarios in complicated quantum networks.
Device-independent self-testing refers to the certification of quantum states based entirely on the correlations exhibited by measurements on separate subsystems. The fact that such a certification is possible at all is remarkable in its own right, and is intimately connected to the violation Bell’s inequalities by entangled quantum systems. In the bipartite case, it is known that, for every pure entangled bipartite state, there exists a device-independent self-testing protocol. Despite the growing interest in self-testing, an analogous universal result in the multipartite setting has remained elusive. In this work, we prove such a universal result for qubits: for every pure n-qubit entangled state, we give an explicit Bell-scenario correlations that self-tests that state, up to local isometries and, where relevant, complex conjugation. The authors prove that any pure entangled state of multiple quantum bits (qubits) can be uniquely identified using only measurement statistics, without trusting the devices, resolving a long-standing open problem in quantum certification.