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Network-assist free self-testing of genuine multipartite entangled states

Ranendu Adhikary, Abhishek Mishra, Ramij Rahaman

TL;DR

This work addresses device-independent self-testing of genuine multipartite entangled states using Hardy's nonlocality argument, avoiding network assistance and bipartite entangled measurements. It analytically constructs the unique $n$-qubit Hardy state $| olinebreak psi^H_n angle$ that self-tests under maximal Hardy probability and derives a device-independent bound $p_{ ext{max}}$ for the generalized test. In a noise-tolerant extension for three parties, the authors use the NPA hierarchy to bound quantum correlations and show no dimensional advantage beyond three qubits, with a device-independent maximum Hardy probability of about $0.018$ in the tripartite case. The work has implications for secure quantum tasks and foundational studies by enabling true multipartite, device-independent self-testing.

Abstract

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.

Network-assist free self-testing of genuine multipartite entangled states

TL;DR

This work addresses device-independent self-testing of genuine multipartite entangled states using Hardy's nonlocality argument, avoiding network assistance and bipartite entangled measurements. It analytically constructs the unique -qubit Hardy state that self-tests under maximal Hardy probability and derives a device-independent bound for the generalized test. In a noise-tolerant extension for three parties, the authors use the NPA hierarchy to bound quantum correlations and show no dimensional advantage beyond three qubits, with a device-independent maximum Hardy probability of about in the tripartite case. The work has implications for secure quantum tasks and foundational studies by enabling true multipartite, device-independent self-testing.

Abstract

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.
Paper Structure (6 sections, 2 theorems, 16 equations, 1 figure)

This paper contains 6 sections, 2 theorems, 16 equations, 1 figure.

Table of Contents

  1. Introduction.
  2. Hardy's non-locality argument
  3. $n$-qubit states showing Hardy's non-locality
  4. True Hardy argument in realistic noise-tolerance scenario
  5. Conclusion
  6. Acknowledgement.

Key Result

Theorem 1

In an $n$-partite Hardy test (MHardyn), if the success probability attains its maximum value $p_{max}$, then the state of the system is equivalent up to local unitaries to $\ket{\psi^H_n}\bra{\psi^H_n}\otimes \varrho'$, where $\varrho'$ is an arbitrary $n$-partite junk state.

Figures (1)

  • Figure 1: Plot of maximum probability of success ($p_{Hardy}$) of tripartite Hardy's argument against the noise parameter $\epsilon$ under different scenario.

Theorems & Definitions (2)

  • Theorem 1
  • Theorem 2