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arXiv:2307.06710 · Physical Review A

Certification of two-qubit quantum systems with temporal inequality

Chellasamy Jebarathinam, Gautam Sharma, Sk Sazim, Remigiusz Augusiak

Published Aug 6, 2024• 2 citations
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Abstract

Self-testing of quantum devices based on observed measurement statistics is a method to certify quantum systems using minimal resources. In Irfan et al. [A. A. M. Irfan, K. Mayer, G. Ortiz, and E. Knill, Phys. Rev. A 101, 032106 (2020)] a scheme based on observing measurement statistics that demonstrate Kochen-Specker contextuality has been shown to certify two-qubit entangled states and measurements without the requirement of spatial separation between the subsystems. However, this scheme assumes a set of compatibility conditions on the measurements which are crucial to demonstrating Kochen-Specker contextuality. In this paper, we propose a self-testing protocol to certify the above two-qubit states and measurements without the assumption of the compatibility conditions, and at the same time without requiring the spatial separation between the subsystems. Our protocol is based on the observation of sequential correlations leading to the maximal violation of a temporal inequality derived from noncontextuality inequality. Moreover, our protocol is robust to small experimental errors or noise.

DOI
10.1103/physreva.110.022408

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Self-testing of quantum devices based on observed measurement statistics is a method to certify quantum systems using minimal resources. In Irfan et al. [A. A. M. Irfan, K. Mayer, G. Ortiz, and E. Knill, Phys. Rev. A 101, 032106 (2020)] a scheme based on observing measurement statistics that demonstrate Kochen-Specker contextuality has been shown to certify two-qubit entangled states and measurements without the requirement of spatial separation between the subsystems. However, this scheme assumes a set of compatibility conditions on the measurements which are crucial to demonstrating Kochen-Specker contextuality. In this paper, we propose a self-testing protocol to certify the above two-qubit states and measurements without the assumption of the compatibility conditions, and at the same time without requiring the spatial separation between the subsystems. Our protocol is based on the observation of sequential correlations leading to the maximal violation of a temporal inequality derived from noncontextuality inequality. Moreover, our protocol is robust to small experimental errors or noise.
Abstract Demonstrating contextual correlations in quantum theory through the violation of a non-contextuality inequality necessarily needs some ‘contexts’ and thus assumes some compatibility relations between the measurements. As a result, any self-testing protocol based on the maximal violation of such inequality is not free from such assumptions. In this work, we propose temporal inequalities derived from non-contextuality inequalities for multi-qubit systems without assuming any compatibility relations among the measurements. We demonstrate that the new inequalities can be maximally violated via a sequential measurement scenario. Moreover, using the maximal violation of these temporal inequalities, we are able to certify the multi-qubit Greenberger–Horne–Zeilinger (GHZ) states and the measurements.
Self-testing has been established as a major approach for quantum device certification based on experimental statistics with minimal assumptions. However, despite more than 20 years of research effort, most of the self-testing protocols are restricted to spatial scenarios (Bell scenarios), without many temporal generalizations known. Under the scenario of sequential measurements performed on a single quantum system, semi-definite optimization-based techniques have been applied to bound sequential measurement inequalities. Building upon this formalism, we show that the optimizer matrix that saturates such sequential inequalities is unique and, moreover, this uniqueness is robust to small deviations from the quantum bound. Furthermore, we consider a generalized scenario in the presence of quantum channels and highlight analogies to the structure of Bell and sequential inequalities using the pseudo-density matrix formalism. These analogies allow us to show a practical use of maximal violations of sequential inequalities in the form of certification of quantum channels up to isometries.
We propose a family of noncontextuality inequalities and show that they can be used for certification of multiqubit quantum systems. Our scheme, unlike those based on nonlocality, does not require spatial separation between the subsystems, yet it makes use of certain compatibility relations between measurements. Moreover, it is scalable in the sense that the number of expectation values that are to be measured to observe contextuality scales polynomially with the number of qubits that are being certified. In a particular case we also show our scheme to be robust to errors and experimental imperfections. Our results seem promising as far as certification of physical setups is concerned in scenarios where spatial separation between the subsystems cannot be guaranteed.
Violation of a noncontextuality inequality or the phenomenon referred to `quantum contextuality' is a fundamental feature of quantum theory. In this article, we derive a novel family of noncontextuality inequalities along with their sum-of-squares decompositions in the simplest (odd-cycle) sequential-measurement scenario capable to demonstrate Kochen-Specker contextuality. The sum-of-squares decompositions allow us to obtain the maximal quantum violation of these inequalities and a set of algebraic relations necessarily satisfied by any state and measurements achieving it. With their help, we prove that our inequalities can be used for self-testing of three-dimensional quantum state and measurements. Remarkably, the presented self-testing results rely on a single assumption about the measurement device that is much weaker than the assumptions considered in Kochen-Specker contextuality.
Certification of quantum devices received from unknown providers is a primary requirement before utilizing the devices for any information processing task. Here, we establish a protocol for certification of a particular set of d -outcome quantum measurements (with d being arbitrary) in a setup comprising of a preparation followed by two measurements in sequence. We propose a set of temporal inequalities pertaining to different d involving correlation functions corresponding to successive measurement outcomes, that are not satisfied by quantum devices. Using quantum violations of these inequalities, we certify specific d -outcome quantum measurements under some minimal assumptions which can be met in an experiment efficiently. Our certification protocol neither requires entanglement, nor any prior knowledge about the dimension of the system under consideration. We further show that our protocol is robust against practical non-ideal realizations. Finally, as an offshoot of our protocol, we present a scheme for secure certification of genuine quantum randomness.
Device-independent certification, also known as self-testing, aims at guaranteeing the proper functioning of untrusted and uncharacterized devices. For example, the quality of an unknown source expected to produce two-qubit maximally entangled states can be evaluated in a bipartite scenario, each party using two binary measurements. The most robust approach consists in deducing the fidelity of produced states with respect to a two-qubit maximally entangled state from the violation of the CHSH inequality. In this paper, we show how the self-testing of two-qubit maximally entangled states is improved by a refined analysis of measurement statistics. The use of suitably chosen Bell tests, depending on the observed correlations, allows one to conclude higher fidelities than ones previously known. In particular, nontrivial self-testing statements can be obtained from correlations that cannot be exploited by a CHSH-based self-testing strategy. Our results not only provide insight into the set of quantum correlations suited for self-testing, but also facilitate the experimental implementations of device-independent certifications.