scholarly journals Robust self-testing of steerable quantum assemblages and its applications on device-independent quantum certification

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 552
Author(s):  
Shin-Liang Chen ◽  
Huan-Yu Ku ◽  
Wenbin Zhou ◽  
Jordi Tura ◽  
Yueh-Nan Chen

Given a Bell inequality, if its maximal quantum violation can be achieved only by a single set of measurements for each party or a single quantum state, up to local unitaries, one refers to such a phenomenon as self-testing. For instance, the maximal quantum violation of the Clauser-Horne-Shimony-Holt inequality certifies that the underlying state contains the two-qubit maximally entangled state and the measurements of one party contains a pair of anti-commuting qubit observables. As a consequence, the other party automatically verifies the set of states remotely steered, namely the "assemblage", is in the eigenstates of a pair of anti-commuting observables. It is natural to ask if the quantum violation of the Bell inequality is not maximally achieved, or if one does not care about self-testing the state or measurements, are we capable of estimating how close the underlying assemblage is to the reference one? In this work, we provide a systematic device-independent estimation by proposing a framework called "robust self-testing of steerable quantum assemblages". In particular, we consider assemblages violating several paradigmatic Bell inequalities and obtain the robust self-testing statement for each scenario. Our result is device-independent (DI), i.e., no assumption is made on the shared state and the measurement devices involved. Our work thus not only paves a way for exploring the connection between the boundary of quantum set of correlations and steerable assemblages, but also provides a useful tool in the areas of DI quantum certification. As two explicit applications, we show 1) that it can be used for an alternative proof of the protocol of DI certification of all entangled two-qubit states proposed by Bowles et al., and 2) that it can be used to verify all non-entanglement-breaking qubit channels with fewer assumptions compared with the work of Rosset et al.

Quantum ◽  
2019 ◽  
Vol 3 ◽  
pp. 198 ◽  
Author(s):  
Jędrzej Kaniewski ◽  
Ivan Šupić ◽  
Jordi Tura ◽  
Flavio Baccari ◽  
Alexia Salavrakos ◽  
...  

Bell inequalities are an important tool in device-independent quantum information processing because their violation can serve as a certificate of relevant quantum properties. Probably the best known example of a Bell inequality is due to Clauser, Horne, Shimony and Holt (CHSH), which is defined in the simplest scenario involving two dichotomic measurements and whose all key properties are well understood. There have been many attempts to generalise the CHSH Bell inequality to higher-dimensional quantum systems, however, for most of them the maximal quantum violation---the key quantity for most device-independent applications---remains unknown. On the other hand, the constructions for which the maximal quantum violation can be computed, do not preserve the natural property of the CHSH inequality, namely, that the maximal quantum violation is achieved by the maximally entangled state and measurements corresponding to mutually unbiased bases. In this work we propose a novel family of Bell inequalities which exhibit precisely these properties, and whose maximal quantum violation can be computed analytically. In the simplest scenario it recovers the CHSH Bell inequality. These inequalities involve d measurements settings, each having d outcomes for an arbitrary prime number d≥3. We then show that in the three-outcome case our Bell inequality can be used to self-test the maximally entangled state of two-qutrits and three mutually unbiased bases at each site. Yet, we demonstrate that in the case of more outcomes, their maximal violation does not allow for self-testing in the standard sense, which motivates the definition of a new weak form of self-testing. The ability to certify high-dimensional MUBs makes these inequalities attractive from the device-independent cryptography point of view.


2014 ◽  
Vol 12 (06) ◽  
pp. 1450040
Author(s):  
Xu Chen ◽  
Hong-Yi Su ◽  
Zhen-Peng Xu ◽  
Yu-Chun Wu ◽  
Jing-Ling Chen

Homogenization proposed in [Y.-C Wu and M. Żukowski, Phys. Rev. A 85 (2012) 022119] is a procedure to transform a tight Bell inequality with partial correlations into a full-correlation form that is also tight. In this paper, we check the homogenizations of two families of n-partite Bell inequalities: the Hardy inequality and the tight Bell inequality without quantum violation. For Hardy's inequalities, their homogenizations bear stronger quantum violation for the maximally entangled state; the tight Bell inequalities without quantum violation give the boundary of quantum and supra-quantum, but their homogenizations do not have the similar properties. We find their homogenization are violated by the maximally entangled state. Numerically computation shows the the domains of quantum violation of homogenized Hardy's inequalities for the generalized GHZ states are smaller than those of Hardy's inequalities.


2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Shubhayan Sarkar ◽  
Debashis Saha ◽  
Jędrzej Kaniewski ◽  
Remigiusz Augusiak

AbstractBell nonlocality as a resource for device-independent certification schemes has been studied extensively in recent years. The strongest form of device-independent certification is referred to as self-testing, which given a device, certifies the promised quantum state as well as quantum measurements performed on it without any knowledge of the internal workings of the device. In spite of various results on self-testing protocols, it remains a highly nontrivial problem to propose a certification scheme of qudit–qudit entangled states based on violation of a single d-outcome Bell inequality. Here we address this problem and propose a self-testing protocol for the maximally entangled state of any local dimension using the minimum number of measurements possible, i.e., two per subsystem. Our self-testing result can be used to establish unbounded randomness expansion, $${{{\mathrm{log}}}\,}_{2}d$$ log 2 d perfect random bits, while it requires only one random bit to encode the measurement choice.


2003 ◽  
Vol 3 (2) ◽  
pp. 157-164
Author(s):  
H. Bechmann-Pasquinucci ◽  
N. Gisin

We present a generalized Bell inequality for two entangled quNits. On one quNit the choice is between two standard von Neumann measurements, whereas for the other quNit there are N^2 different binary measurements. These binary measurements are related to the intermediate states known from eavesdropping in quantum cryptography. The maximum violation by \sqrt{N} is reached for the maximally entangled state. Moreover, for N=2 it coincides with the familiar CHSH-inequality.


Pramana ◽  
2001 ◽  
Vol 56 (2-3) ◽  
pp. 153-159 ◽  
Author(s):  
M Genovese ◽  
G Brida ◽  
C Novero ◽  
E Predazzi

2019 ◽  
Vol 74 (6) ◽  
pp. 523-537
Author(s):  
Jyoti Faujdar ◽  
Atul Kumar

AbstractIn this article, we revisit the question of analysing the efficiencies of partially entangled states in three-qubit classes under real conditions. Our results show some interesting observations regarding the efficiencies and correlations of partially entangled states. Surprisingly, we find that the efficiencies of many three-qubit partially entangled states exceed that of maximally entangled three-qubit states under real noisy conditions and applications of weak measurements. Our analysis, therefore, suggests that the efficiencies of partially entangled states are much more robust to noise than those of maximally entangled states at least for the GHZ (Greenberger–Horne–Zeilinger) class states, for certain protocols; i.e. less correlations in the initially prepared state may also lead to better efficiency and hence one need not always consider starting with a maximally entangled state with maximum correlations between the qubits. For a set of partially entangled states, we find that the efficiency is optimal, independent of the decoherence and state parameters, if the value of weak measurement parameter is very large. For other values of the weak measurement parameter, the robustness of the states depends on the decoherence and state parameters. Moreover, we further show that one can achieve higher efficiencies in a protocol by using non-optimal weak measurement strengths instead of optimal weak measurement strengths.


Quantum ◽  
2022 ◽  
Vol 6 ◽  
pp. 614
Author(s):  
Honghao Fu

Let p be an odd prime and let r be the smallest generator of the multiplicative group Zp∗. We show that there exists a correlation of size Θ(r2) that self-tests a maximally entangled state of local dimension p−1. The construction of the correlation uses the embedding procedure proposed by Slofstra (Forum of Mathematics, Pi. (2019)). Since there are infinitely many prime numbers whose smallest multiplicative generator is in the set {2,3,5} (D.R. Heath-Brown The Quarterly Journal of Mathematics (1986) and M. Murty The Mathematical Intelligencer (1988)), our result implies that constant-sized correlations are sufficient for self-testing of maximally entangled states with unbounded local dimension.


2004 ◽  
Vol 02 (01) ◽  
pp. 23-31 ◽  
Author(s):  
ANTONIO ACÍN ◽  
NICOLAS GISIN ◽  
LLUIS MASANES ◽  
VALERIO SCARANI

We review the status of Bell's inequalities in quantum information, stressing mainly the links with quantum key distribution and distillation of entanglement. We also prove that for all the eavesdropping attacks using one qubit, and for a family of attacks of two qubits, acting on half of a maximally entangled state of two qubits, the violation of a Bell inequality implies the possibility of an efficient secret-key extraction.


2020 ◽  
Vol 34 (05) ◽  
pp. 2050067
Author(s):  
Yan-Jie Zhang ◽  
Cai-Peng Shen ◽  
Zhi-Feng Pan ◽  
Ya Gao ◽  
Shi-Lei Su ◽  
...  

An entanglement concentration protocol in photonic collective-rotating decoherence-free subspace (CRDFS) is proposed. To accomplish the scheme, two methods to construct parity measurement devices in CRDFS are presented by exploiting the cross-Kerr nonlinearity, through which partially entangled states are converted to maximally entangled states. The performance of the protocol can be improved by iteration method. Fidelity in consideration of dissipation is discussed, which demonstrates good robustness. In contrast to the conventional protocols, the present one has distinctive feature since it can not only get maximally entangled state from less entangled state, but also maintain the maximal entanglement in collective-rotating noise environment.


2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Marcin Wieśniak

AbstractQuantum correlations, in particular those, which enable to violate a Bell inequality, open a way to advantage in certain communication tasks. However, the main difficulty in harnessing quantumness is its fragility to, e.g, noise or loss of particles. We study the persistency of Bell correlations of GHZ based mixtures and Dicke states. For the former, we consider quantum communication complexity reduction (QCCR) scheme, and propose new Bell inequalities (BIs), which can be used in that scheme for higher persistency in the limit of large number of particles N. In case of Dicke states, we show that persistency can reach 0.482N, significantly more than reported in previous studies.


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