Scalable Bell Inequalities for Qubit Graph States and Robust Self-Testing

Baccari, F.; Augusiak, Remigiusz; Šupić, Ivan; Tura, Jordi; Acín, Antonio

doi:10.1103/physrevlett.124.020402

Cited by 66 publications

(92 citation statements)

References 47 publications

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“…Recently, we became aware of the work of Ref. [52] which also discussed the construction of two-setting Bell inequalities that are maximally violated by given graph states. Before giving the proofs of local bounds, let us remind that L is a convex polytope and that the Bell expressions considered here are linear in E n ( x) (and thus in P ).…”

Section: Discussionmentioning

confidence: 99%

Exploring Bell inequalities for the device-independent certification of multipartite entanglement depth

et al. 2019

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Techniques developed for device-independent characterizations allow one to certify certain physical properties of quantum systems without assuming any knowledge of their internal workings. Such a certification, however, often relies on the employment of device-independent witnesses catered for the particular property of interest. In this work, we consider a one-parameter family of multipartite, two-setting, two-outcome Bell inequalities and demonstrate the extent to which they are suited for the device-independent certification of genuine many-body entanglement (and hence the entanglement depth) present in certain well-known multipartite quantum states, including the generalized Greenberger-Horne-Zeilinger (GHZ) states with unbalanced weights, the higher-dimensional generalizations of balanced GHZ states, and the W states. As a by-product of our investigations, we have found that, in contrast with well-established results, provided trivial qubit measurements are allowed, full-correlation Bell inequalities can also be used to demonstrate the nonlocality of weakly entangled unbalanced-weight GHZ states. Besides, we also demonstrate how two-setting, two-outcome Bell inequalities can be constructed, based on the so-called GHZ paradox, to witness the entanglement depth of various graph states, including the ring graph states, the fully connected graph states, and some linear graph states, etc.

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Section: Discussionmentioning

confidence: 99%

Exploring Bell inequalities for the device-independent certification of multipartite entanglement depth

et al. 2019

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“…Due to insufficient quantum capability of the client, the client cannot verify the correctness of the calculation. Therefore, several verifiable BQC (VBQC) protocols have been proposed 15‐27 . In 2015, Hayashi and Morimae proposed a VBQC protocol by utilizing the stabilizer test verification 20 .…”

Section: Introductionmentioning

confidence: 99%

A simplified verifiable blind quantum computing protocol with quantum input verification

Quan

Liu³

et al. 2021

Quantum Engineering

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Blind quantum computing (BQC) enables a client with limited quantum capability to delegate her quantum computation to a remote quantum server and still keeps the client's input, output, and the algorithm private. One important property of BQC is verifiability, which means the client can verify the correctness of the computation or unknown quantum inputs. Recently, Morimae proposed a verifiable blind quantum computing protocol where the client can verify both the correctness of computing and the quantum input. However, the client needs much quantum memory and takes a lot of qubits to get the true result. We reduce the size of quantum memory and the number of qubits used in Morimae's protocol. Besides, we extend the resource state in Morimae's protocol from graph state to hypergraph state. For certain hypergraph states as resources states, such as Union Jack State, the client only needs Pauli measurements in the computation stage but he needs non‐Clifford basis measurements if graph states are considered as resources states.

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“…In most protocols, the proofs for self-testing rely on the maximal violation of the Bell inequalities. However, even in the simplest Bell scenario (two parties and two binary measurements on each party), the maximal violation by a partially entangled state is known for only a few Bell inequalities [9][10][11][12][13], and not many protocols are proposed for selftesting partially entangled states [14][15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, y¢ | | is determined to c cos 2 as in the two-qubit realizations of equation(5). The proof is given in appendix D. The difference from the proof of lemma 2 is that d Bx and d A y by equation(4)are not ensured to coincide with D x B ) , and we cannot use equation(12). For the same reason, F x  and E y  infigure 1are now not ensured to attain D x B and D ; is merely the projection of A x  to the B-plane.In this way, the geometry is uniquely determined for not necessarily = , this uniqueness does not ensure the extremality of  C .…”

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confidence: 97%

Geometrical self-testing of partially entangled two-qubit states

Ishizaka

2020

New J. Phys.

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Quantum nonlocality has recently been intensively studied in connection to device-independent quantum information processing, where the extremal points of the set of quantum correlations play a crucial role through self-testing. In most protocols, the proofs for self-testing rely on the maximal violation of the Bell inequalities, but there is another known proof based on the geometry of state vectors to self-test a maximally entangled state. We present a geometrical proof in the case of partially entangled states. We show that, when a set of correlators in the simplest Bell scenario satisfies a condition, the geometry of the state vectors is uniquely determined. The realization becomes selftestable when another unitary observable exists on the geometry. Applying this proven fact, we propose self-testing protocols by intentionally adding one more measurement. This geometrical scheme for self-testing is superior in that, by using this as a building block and repeatedly adding measurements, a realization with an arbitrary number of measurements can be self-tested. Besides the application, we also attempt to describe nonlocal correlations by guessing probabilities of distant measurement outcomes. In this description, the quantum set is also convex, and a large class of extremal points is identified by the uniqueness of the geometry.

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Scalable Bell Inequalities for Qubit Graph States and Robust Self-Testing

Cited by 66 publications

References 47 publications

Exploring Bell inequalities for the device-independent certification of multipartite entanglement depth

Exploring Bell inequalities for the device-independent certification of multipartite entanglement depth

A simplified verifiable blind quantum computing protocol with quantum input verification

Geometrical self-testing of partially entangled two-qubit states

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