scholarly journals Three-observer Bell inequality violation on a two-qubit entangled state

2017 ◽  
Vol 2 (1) ◽  
pp. 015010 ◽  
Author(s):  
Matteo Schiavon ◽  
Luca Calderaro ◽  
Mirko Pittaluga ◽  
Giuseppe Vallone ◽  
Paolo Villoresi
Keyword(s):  
Bell Inequality ◽  
Entangled State

scholarly journals Measurement of entropy and quantum coherence properties of two type-I entangled photonic qubits

2021 ◽  
Vol 53 (7) ◽  
Author(s):  
Ali Motazedifard ◽  
Seyed Ahmad Madani ◽  
N. S. Vayaghan
Keyword(s):  
Maximum Likelihood ◽  
Quantum Coherence ◽  
Single Photon ◽  
Bell Inequality ◽  
Bell State ◽  
Von Neumann Entropy ◽  
Entangled State ◽  
Type I ◽  
Variable Theory ◽  
High Brightness

AbstractUsing the type-I SPDC process in BBO nonlinear crystal, we generate a polarization-entangled state near to the maximally-entangled Bell-state with high-visibility (high-brightness) 98.50 ± 1.33% (87.71 ± 4.45%) for HV (DA) basis. We calculate the CHSH version of the Bell inequality, as a nonlocal realism test, and find a strong violation from the classical physics or any hidden variable theory, S = 2.71 ± 0.10. Via measuring the coincidence count rate in the SPDC process, we obtain the quantum efficiency of single-photon detectors around (25.5 ± 3.4)%, which is in good agreement to their manufacturer company. As expected, we verify the linear dependency of the CC rate vs. pump power of input CW-laser, which may yield to find the effective second-order susceptibility crystal. Using the theory of the measurement of qubits, includes a tomographic reconstruction of quantum states due to the linear set of 16 polarization-measurement, together with a maximum-likelihood-technique, which is based on the numerical optimization, we calculate the physical non-negative definite density matrices, which implies on the non-separability and entanglement of prepared state. By having the maximum likelihood density operator, we calculate precisely the entanglement measures such as Concurrence, entanglement of formation, tangle, logarithmic negativity, and different entanglement entropies such as linear entropy, Von-Neumann entropy, and Renyi 2-entropy. Finally, this high-brightness and low-rate entangled photons source can be used for short-range quantum measurements in the Lab.

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.

scholarly journals Entangled-state generation and Bell inequality violations in nanomechanical resonators

2014 ◽  
Vol 90 (17) ◽  
Author(s):  
J. Robert Johansson ◽  
Neill Lambert ◽  
Imran Mahboob ◽  
Hiroshi Yamaguchi ◽  
Franco Nori
Keyword(s):  
Bell Inequality ◽  
Entangled State ◽  
Nanomechanical Resonators ◽  
State Generation ◽  
Entangled State Generation

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 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.

A BELL INEQUALITY BASED ON CORRELATION FUNCTIONS FOR THREE QUBITS

2005 ◽  
Vol 03 (supp01) ◽  
pp. 53-59 ◽  
Author(s):  
CHUNFENG WU ◽  
JING-LING CHEN ◽  
L. C. KWEK ◽  
C. H. OH
Keyword(s):  
Correlation Function ◽  
Correlation Functions ◽  
Bell Inequality ◽  
Entangled State

We discuss a Bell inequality based on correlation function for three qubits. The inequality is violated by any pure entangled state for 3 qubits. The strength of the violation is the same as the result in Ref.13.

Nonlocality, entanglement, and randomness in different conflicting interest Bayesian games

2020 ◽  
Vol 20 (11&12) ◽  
pp. 901-934
Author(s):  
Hargeet Kaur ◽  
Atul Kumar
Keyword(s):  
Mixed State ◽  
Bell Inequality ◽  
Bell State ◽  
Coordination Games ◽  
Common Interest ◽  
Entangled State ◽  
Bayesian Games ◽  
Bayesian Game ◽  
Shared Resource ◽  
Quantum Strategies

We analyse different Bayesian games where payoffs of players depend on the types of players involved in a two-player game. The dependence is assumed to commensurate with the CHSH game setting. For this, we consider two different types of each player (Alice and Bob) in the game, thus resulting in four different games clubbed together as one Bayesian game. Considering different combinations of common interest, and conflicting interest coordination and anti-coordination games, we find that quantum strategies are always preferred over classical strategies if the shared resource is a pure non-maximally entangled state. However, when the shared resource is a class of mixed state, then quantum strategies are useful only for a given range of the state parameter. Surprisingly, when all conflicting interest games (Battle of the Sexes game and Chicken game) are merged into the Bayesian game picture, then the best strategy for Alice and Bob is to share a set of non-maximally entangled pure states. We demonstrate that this set not only gives higher payoff than any classical strategy, but also outperforms a maximally entangled pure Bell state, mixed Werner states, and Horodecki states. We further propose the representation of a special class of Bell inequality- tilted Bell inequality, as a common as well as conflicting interest Bayesian game. We thereafter, study the effect of sharing an arbitrary two-qubit pure state and a class of mixed state as quantum resource in those games; thus verifying that non-maximally entangled states with high randomness help attain maximum quantum benefit. Additionally, we propose a general framework of a two-player Bayesian game for d-dimensions Bell-CHSH inequality, with and without the tilt factor.

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 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.

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