Self-testing using only marginal information

Li, Xinhui; Cai, Yu; Han, Yong; Wen, Qiao Yan; Scarani, Valerio

doi:10.1103/physreva.98.052331

Cited by 11 publications

(4 citation statements)

References 27 publications

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“…Suppose the channel suffers with white noise (weight ), one can transform the problem of robustness into the problem that finding a lower bound on the fidelity. It can be solved by SDP [24,[42][43][44]:…”

Section: Robust Self-testing Of the Gsmmentioning

confidence: 99%

Robust self-testing of multipartite GHZ-state measurements in quantum networks

Zhou¹,

Xu²,

Zhen³

et al. 2021

Preprint

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Self-testing is a device-independent examination of quantum devices based on correlations of observed statistics. Motivated by elegant progresses on selftesting strategies for measurements [Phys. Rev. Lett. 121, 250507 (2018)] and for states [New J. Phys. 20, 083041 (2018)], we develop a general self-testing procedure for multipartite generalized GHZ-state measurements. The key step is self-testing all measurement eigenstates for a general N −qubit multipartite GHZ-state measurement. Following our procedure, one only needs to perform local measurements on N − 2 chosen parties of the N -partite eigenstate and maintain to achieve the maximal violation of tilted Clauser-Horne-Shimony-Holt (CHSH) Bell inequality for remaining two parties. Moreover, this approach is physically operational from an experimental point of view. It turns out that the existing result for three-qubit GHZ-state measurement is recovered as a special case. Meanwhile, we develop the self-testing method to be robust against certain white noise.

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Section: Robust Self-testing Of the Gsmmentioning

confidence: 99%

Robust self-testing of multipartite GHZ-state measurements in quantum networks

Zhou¹,

Xu²,

Zhen³

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…Nevertheless, these schemes use full-body correlators and require individual addressing, thus being less appealing from an experimental point of view. Therefore, some studies have been carried to find out whether self-testing is possible using only marginal information [80] (see also [81,82]): In [80], some efforts showed that the three-qubit states maximally violating some of the translationally invariant, two-body Bell inequalities from [83] could be self-tested using two-body correlators, thus giving a positive answer to this question.…”

Section: Lemmamentioning

confidence: 99%

The quantum marginal problem for symmetric states: applications to variational optimization, nonlocality and self-testing

Aloy,

Fadel,

Tura

2020

Preprint

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In this paper, we present a method to solve the quantum marginal problem for symmetric d-level systems. The method is built upon an efficient semi-definite program that determines the compatibility conditions of an m-body reduced density with a global n-body density matrix supported on the symmetric space. We illustrate the applicability of the method in central quantum information problems with several exemplary case studies. Namely, (i) a fast variational ansatz to optimize local Hamiltonians over symmetric states, (ii) a method to optimize symmetric, few-body Bell operators over symmetric states and (iii) a set of sufficient conditions to determine which symmetric states cannot be self-tested from few-body observables. As a by-product of our findings, we also provide a generic, analytical correspondence between arbitrary superpositions of n-qubit Dicke states and translationally-invariant diagonal matrix product states of bond dimension n.

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“…The method of inferring more detailed properties of a quantum experiment in a black-box scenario is referred to as "self-testing" [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29]. Mayer and Yao [30] first proposed such a deviceindependent method for certifying any type of quantum system.…”

Section: Introductionmentioning

confidence: 99%

Experimental self-testing for photonic graph states

Xu,

Zhou,

Yang

et al. 2021

Preprint

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Graph states-one of the most representative families of multipartite entangled states, are important resources for multiparty quantum communication, quantum error correction, and quantum computation. Device-independent certification of highly entangled graph states plays a prominent role in the quantum information processing tasks. Here we have experimentally demonstrated device-independent certification for multipartite graph states, by adopting the robust self-testing scheme based on scalable Bell inequalities. Specifically, the prepared multi-qubit Greenberger-Horne-Zeilinger (GHZ) states and linear cluster states achieve a high degree of Bell violation, which are beyond the nontrivial bounds of the robust self-testing scheme. Furthermore, our work paves the way to the device-independent certification of complex multipartite quantum states.

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Self-testing using only marginal information

Cited by 11 publications

References 27 publications

Robust self-testing of multipartite GHZ-state measurements in quantum networks

Robust self-testing of multipartite GHZ-state measurements in quantum networks

The quantum marginal problem for symmetric states: applications to variational optimization, nonlocality and self-testing

Experimental self-testing for photonic graph states

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