scholarly journals What is the minimum CHSH score certifying that a state resembles the singlet?

Quantum ◽  
2020 ◽  
Vol 4 ◽  
pp. 246 ◽  
Author(s):  
Xavier Valcarce ◽  
Pavel Sekatski ◽  
Davide Orsucci ◽  
Enky Oudot ◽  
Jean-Daniel Bancal ◽  
...  
Keyword(s):  
Quantum State ◽  
Analytical Approach ◽  
Singlet State ◽  
Bell Inequality ◽  
Sharp Contrast ◽  
Independent State ◽  
Internal Working ◽  
Chsh Inequality ◽  
Local Bound ◽  
Measured State

A quantum state can be characterized from the violation of a Bell inequality. The well-known CHSH inequality for example can be used to quantify the fidelity (up to local isometries) of the measured state with respect to the singlet state. In this work, we look for the minimum CHSH violation leading to a non-trivial fidelity. In particular, we provide a new analytical approach to explore this problem in a device-independent framework, where the fidelity bound holds without assumption about the internal working of devices used in the CHSH test. We give an example which pushes the minimum CHSH threshold from ≈2.0014 to ≈2.05, far from the local bound. This is in sharp contrast with the device-dependent (two-qubit) case, where entanglement is one-to-one related to a non-trivial singlet fidelity. We discuss this result in a broad context including device-dependent/independent state characterizations with various classical resources.

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.

Dynamics of bell-nonlocality for two atoms interacting with a vacuum multi-mode noise field

2016 ◽  
Vol 14 (03) ◽  
pp. 1650011 ◽  
Author(s):  
Yu-Jie Liu ◽  
Li Zheng ◽  
Dong-Mei Han ◽  
Huan-Lin Lü ◽  
Tai-Yu Zheng
Keyword(s):  
Degrees Of Freedom ◽  
Internal State ◽  
Bell Inequality ◽  
Entanglement Dynamics ◽  
Noise Field ◽  
Chsh Inequality ◽  
Internal States ◽  
Bell Nonlocality ◽  
Multi Mode ◽  
Spatial Degrees Of Freedom

We investigate the internal-state Bell nonlocal entanglement dynamics, as measured by CHSH inequality of two atoms interacting with a vacuum multi-mode noise field by taking into account the spatial degrees of freedom of the two atoms. The dynamics of Bell nonlocality of the atoms with the atomic internal states being initially in a Werner-type state is studied, by deriving the analytical solutions of the Schrödinger equation, and tracing over the degrees of freedom of the field and the external motion of the two atoms. In addition, through comparison with entanglement as measured by concurrence, we find that the survival time of entanglement is much longer than that of the Bell-inequality violation. And the comparison of the quantum correlation time between two Werner-type states is discussed.

scholarly journals Challenges in preparing, preserving and detecting para-water in bulk: overcoming proton exchange and other hurdles

2015 ◽  
Vol 17 (40) ◽  
pp. 26819-26827 ◽  
Author(s):  
Daniele Mammoli ◽  
Nicola Salvi ◽  
Jonas Milani ◽  
Roberto Buratto ◽  
Aurélien Bornet ◽  
...  
Keyword(s):  
Quantum State ◽  
Singlet State ◽  
Proton Exchange

Para-water is an analogue of para-hydrogen, where the two proton spins are in a quantum state that is antisymmetric under permutation, also known as singlet state.

ENTANGLEMENT, PURITY AND VIOLATION OF BELL INEQUALITY

2009 ◽  
Vol 07 (07) ◽  
pp. 1313-1320 ◽  
Author(s):  
DONG-LING DENG ◽  
JING-LING CHEN
Keyword(s):  
Bell Inequality ◽  
The Other ◽  
Two Dimensional ◽  
Entanglement Of Formation ◽  
Other Hand ◽  
Chsh Inequality ◽  
The One ◽  
The Relationship ◽  
Qubit States

We use the Clauser–Horne–Shimony-Holt (CHSH) inequality to investigate the relationship among entanglement, purity and violation of the Bell inequality. On the one hand, we show numerically that all two-dimensional (qubit) states, whose entanglement of formation (EOF) is larger than [Formula: see text], violate the CHSH inequality. On the other hand, any state with purity smaller than 0.5562 may not violate it.

scholarly journals Experimental violation of a d-dimensional Bell inequality using energy-time entangled photons

2014 ◽  
Vol 12 (07n08) ◽  
pp. 1560026 ◽  
Author(s):  
Sacha Schwarz ◽  
Bänz Bessire ◽  
André Stefanov
Keyword(s):  
Frequency Spectrum ◽  
Quantum State ◽  
Spatial Light Modulator ◽  
Bell Inequality ◽  
Entangled Photons ◽  
Light Modulator ◽  
Quantum State Tomography ◽  
State Tomography

We experimentally study the violation of the CGLMP inequality for entangled 2-qubit and 2-qutrit states with different degrees of entanglement using numerically optimized measurement settings. The qudits are encoded and manipulated in the frequency spectrum of broadband energy-time entangled photons by taking into account a spatial light modulator (SLM). The latter allows to discretize the spectrum into bins. By controlling each frequency bin individually, the generation of maximally and non-maximally entangled qutrits is verified through quantum state tomography (QST).

Complementarity between signaling and local indeterminacy

2015 ◽  
Vol 15 (3&4) ◽  
pp. 308-315
Author(s):  
S. Aravinda ◽  
R. Srikanth
Keyword(s):  
Quantum Mechanics ◽  
Singlet State ◽  
Bell’S Theorem ◽  
Bell's Theorem ◽  
Chsh Inequality ◽  
Local Indeterminacy ◽  
No Signaling

The correlations that violate the CHSH inequality are known to have complementary contributions from signaling and local indeterminacy. This complementarity is shown to represent a strengthening of Bell's theorem, and can be used to certify randomness in a device-independent way, assuming neither the validity of quantum mechanics nor even no-signaling. We obtain general nonlocal resources that can simulate the statistics of the singlet state, encompassing existing results. We prove a conjecture due to Hall (2010) and Kar et al. (2011) on the complementarity for such resources.

scholarly journals Simulation of the Bell inequality violation based on quantum steering concept

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Mohsen Ruzbehani
Keyword(s):  
Quantum Mechanics ◽  
Bell Inequality ◽  
Mathematical Formalism ◽  
Bell’S Inequality ◽  
Detector Efficiency ◽  
Bell's Inequality ◽  
Chsh Inequality ◽  
Quantum Steering ◽  
The Given

AbstractViolation of Bell’s inequality in experiments shows that predictions of local realistic models disagree with those of quantum mechanics. However, despite the quantum mechanics formalism, there are debates on how does it happen in nature. In this paper by use of a model of polarizers that obeys the Malus’ law and quantum steering concept, i.e. superluminal influence of the states of entangled pairs to each other, simulation of phenomena is presented. The given model, as it is intended to be, is extremely simple without using mathematical formalism of quantum mechanics. However, the result completely agrees with prediction of quantum mechanics. Although it may seem trivial, this model can be applied to simulate the behavior of other not easy to analytically evaluate effects, such as deficiency of detectors and polarizers, different value of photons in each run and so on. For example, it is demonstrated, when detector efficiency is 83% the S factor of CHSH inequality will be 2, which completely agrees with famous detector efficiency limit calculated analytically. Also, it is shown in one-channel polarizers the polarization of absorbed photons, should change to the perpendicular of polarizer angle, at very end, to have perfect violation of the Bell inequality (2 $$\sqrt 2$$ 2 ) otherwise maximum violation will be limited to (1.5 $$\sqrt{2}$$ 2 ).

scholarly journals Protective Measurement—A New Quantum Measurement Paradigm: Detailed Description of the First Realization

2021 ◽  
Vol 11 (9) ◽  
pp. 4260
Author(s):  
Enrico Rebufello ◽  
Fabrizio Piacentini ◽  
Alessio Avella ◽  
Rudi Lussana ◽  
Federica Villa ◽  
...  
Keyword(s):  
Quantum Measurement ◽  
Single Particle ◽  
Weak Interactions ◽  
Sharp Contrast ◽  
Protection Mechanism ◽  
Expectation Value ◽  
Measurement Protocol ◽  
Quantum Technology ◽  
First Time ◽  
Measured State

We present a detailed description of the experiment realizing for the first time a protective measurement, a novel measurement protocol which combines weak interactions with a “protection mechanism” preserving the measured state coherence during the whole measurement process. Furthermore, protective measurement allows finding the expectation value of an observable, i.e., an inherently statistical quantity, by measuring a single particle, without the need for any statistics. This peculiar property, in sharp contrast to the framework of traditional (projective) quantum measurement, might constitute a groundbreaking advance for several quantum technology related fields.

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