scholarly journals Quantum nonlocality enhanced by homogenization

2014 ◽  
Vol 12 (06) ◽  
pp. 1450040
Author(s):  
Xu Chen ◽  
Hong-Yi Su ◽  
Zhen-Peng Xu ◽  
Yu-Chun Wu ◽  
Jing-Ling Chen
Keyword(s):  
Hardy Inequality ◽  
Bell Inequality ◽  
Bell Inequalities ◽  
Quantum Nonlocality ◽  
Entangled State ◽  
Maximally Entangled State ◽  
Ghz States ◽  
Partial Correlations ◽  
Hardy’S Inequalities ◽  
The Hardy Inequality

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.

scholarly journals Maximal nonlocality from maximal entanglement and mutually unbiased bases, and self-testing of two-qutrit quantum systems

Quantum ◽  
2019 ◽  
Vol 3 ◽  
pp. 198 ◽  
Author(s):  
Jędrzej Kaniewski ◽  
Ivan Šupić ◽  
Jordi Tura ◽  
Flavio Baccari ◽  
Alexia Salavrakos ◽  
...  
Keyword(s):  
Quantum Information Processing ◽  
Bell Inequality ◽  
Bell Inequalities ◽  
Weak Form ◽  
Quantum Systems ◽  
Point Of View ◽  
Entangled State ◽  
Mutually Unbiased Bases ◽  
Maximally Entangled State ◽  
Self Testing

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.

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
Keyword(s):  
Bell Inequality ◽  
Bell Inequalities ◽  
Alternative Proof ◽  
Entangled State ◽  
Maximally Entangled State ◽  
Self Testing ◽  
Measurement Devices ◽  
Shared State ◽  
Qubit States ◽  
Single Set

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.

Bell inequality for quNits with binary measurements

2003 ◽  
Vol 3 (2) ◽  
pp. 157-164
Author(s):  
H. Bechmann-Pasquinucci ◽  
N. Gisin
Keyword(s):  
Quantum Cryptography ◽  
Bell Inequality ◽  
The Other ◽  
Entangled State ◽  
Maximally Entangled State ◽  
Von Neumann ◽  
Chsh Inequality ◽  
Intermediate States ◽  
Von Neumann Measurements

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.

QUANTUM TELEPORTATION OF AN ARBITRARY N-QUBIT STATE VIA NON-MAXIMALLY ENTANGLED STATE

2007 ◽  
Vol 05 (05) ◽  
pp. 673-683 ◽  
Author(s):  
YU-LING LIU ◽  
ZHONG-XIAO MAN ◽  
YUN-JIE XIA
Keyword(s):  
Quantum Teleportation ◽  
Success Probability ◽  
Qubit State ◽  
Bell States ◽  
Entangled State ◽  
Quantum Channels ◽  
Maximally Entangled State ◽  
Ghz States ◽  
Measurement Basis ◽  
Unit Probability

We explicitly present two schemes for quantum teleportation of an arbitrary N-qubit entangled state using, respectively, non-maximally entangled Bell states and GHZ states as the quantum channels, and generalized Bell states as the measurement basis. The scheme succeeds with unit fidelity but less than unit probability. By introducing additional qubit and unitary operations, the success probability of these two schemes can be increased.

scholarly journals First experimental test of bell inequalities performed using a non-maximally entangled state

Pramana ◽  
2001 ◽  
Vol 56 (2-3) ◽  
pp. 153-159 ◽  
Author(s):  
M Genovese ◽  
G Brida ◽  
C Novero ◽  
E Predazzi
Keyword(s):  
Experimental Test ◽  
Bell Inequalities ◽  
Entangled State ◽  
Maximally Entangled State

PERFECT TELEPORTATION OF UNKNOWN QUDIT BY A d-LEVEL GHZ CHANNEL

2009 ◽  
Vol 07 (04) ◽  
pp. 755-770 ◽  
Author(s):  
YINXIANG LONG ◽  
DAOWEN QIU ◽  
DONGYANG LONG
Keyword(s):  
General Scheme ◽  
Bell State ◽  
Ghz State ◽  
Quantum States ◽  
Entangled State ◽  
Input State ◽  
Quantum Channels ◽  
Maximally Entangled State ◽  
Ghz States ◽  
Measurement Basis

In the past decades, various schemes of teleportation of quantum states through different types of quantum channels (a prior shared entangled state between the sender and the receiver), e.g. EPR pairs, generalized Bell states, qubit GHZ states, standard W states and its variations, genuine multiqubit entanglement states, etc., have been developed. Recently, three-qutrit quantum states and two-qudit quantum states have also been considered as quantum channels for teleportation. In this paper, we investigate the teleportation of an unknown qudit using a d level GHZ state, i.e. a three-qudit maximally entangled state, as quantum channel. We design a general scheme of faithful teleportation of an unknown qudit using a d-level GHZ state shared between the sender and the receiver, or among the sender, the receiver and the controller; an unknown two-qudit of Schmidt form using a d level GHZ state shared between the sender and the receiver; as well as an unknown arbitrary two-qudit using two shared d level GHZ states between the sender, the receiver and the controller, or using one shared d level GHZ state and one shared generalized Bell state. We obtain the general formulas of Alice's measurement basis, Charlie's measurement basis and Bob's unitary operations to recover the input state of Alice. It is intuitionistic to generalize the protocols of teleporting an arbitrary two-qudit state to teleporting an arbitrary n-qudit state.

scholarly journals BELL'S INEQUALITIES DETECT EFFICIENT ENTANGLEMENT

2004 ◽  
Vol 02 (01) ◽  
pp. 23-31 ◽  
Author(s):  
ANTONIO ACÍN ◽  
NICOLAS GISIN ◽  
LLUIS MASANES ◽  
VALERIO SCARANI
Keyword(s):  
Quantum Key Distribution ◽  
Bell Inequality ◽  
Entangled State ◽  
Secret Key ◽  
Bell’S Inequalities ◽  
Maximally Entangled State ◽  
The Status ◽  
Bell's Inequalities ◽  
Key Extraction ◽  
Secret Key Extraction

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.

scholarly journals Self-testing quantum systems of arbitrary local dimension with minimal number of measurements

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Shubhayan Sarkar ◽  
Debashis Saha ◽  
Jędrzej Kaniewski ◽  
Remigiusz Augusiak
Keyword(s):  
Bell Inequality ◽  
Quantum Systems ◽  
Entangled State ◽  
Local Dimension ◽  
Maximally Entangled State ◽  
Testing Protocol ◽  
Self Testing ◽  
Minimum Number ◽  
Bell Nonlocality ◽  
Testing Protocols

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.

scholarly journals Geometry and product states

2002 ◽  
Vol 2 (5) ◽  
pp. 333-347
Author(s):  
R.B. Lockhart ◽  
M.J. Steiner ◽  
K. Gerlach
Keyword(s):  
Mixed State ◽  
Convex Combination ◽  
Canonical Decomposition ◽  
Entangled State ◽  
Surprising Result ◽  
Product State ◽  
Maximally Entangled State ◽  
Separable States ◽  
Ghz States

As separable states are a convex combination of product states, the geometry of the manifold of product states, $\Sigma$, is studied. Prior results by Sanpera, Vidal and Tarrach are extended. Furthermore, it is proven that states in the set tangent to $\Sigma$ at the maximally mixed state are separable; the set normal contains, among others, all extended GHZ states. A canonical decomposition is given. A surprising result is that for the case of two particles, the closest product state to the maximally entangled state is the maximally mixed state. An algorithm is provided to find the closest product state.

scholarly journals Mutually unbiased bases and symmetric informationally complete measurements in Bell experiments

2021 ◽  
Vol 7 (7) ◽  
pp. eabc3847
Author(s):  
Armin Tavakoli ◽  
Máté Farkas ◽  
Denis Rosset ◽  
Jean-Daniel Bancal ◽  
Jedrzej Kaniewski
Keyword(s):  
Quantum Key Distribution ◽  
Random Number ◽  
Random Number Generation ◽  
Bell Inequalities ◽  
Extremal Point ◽  
Optimal Rate ◽  
Quantum Nonlocality ◽  
Space Structures ◽  
Mutually Unbiased Bases ◽  
Practical Relevance

Mutually unbiased bases (MUBs) and symmetric informationally complete projectors (SICs) are crucial to many conceptual and practical aspects of quantum theory. Here, we develop their role in quantum nonlocality by (i) introducing families of Bell inequalities that are maximally violated by d-dimensional MUBs and SICs, respectively, (ii) proving device-independent certification of natural operational notions of MUBs and SICs, and (iii) using MUBs and SICs to develop optimal-rate and nearly optimal-rate protocols for device-independent quantum key distribution and device-independent quantum random number generation, respectively. Moreover, we also present the first example of an extremal point of the quantum set of correlations that admits physically inequivalent quantum realizations. Our results elaborately demonstrate the foundational and practical relevance of the two most important discrete Hilbert space structures to the field of quantum nonlocality.

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