scholarly journals Evaluating the Maximal Violation of the Original Bell Inequality by Two-Qudit States Exhibiting Perfect Correlations/Anticorrelations

Entropy ◽  
2018 ◽  
Vol 20 (11) ◽  
pp. 829 ◽  
Author(s):  
Andrei Khrennikov ◽  
Elena Loubenets
Keyword(s):  
Upper Bound ◽  
General Class ◽  
Bell Inequality ◽  
Spin Observable ◽  
Mathematical Study ◽  
Perfect Correlation ◽  
Maximal Violation ◽  
Spin Measurements ◽  
Qubit States

We introduce the general class of symmetric two-qubit states guaranteeing the perfect correlation or anticorrelation of Alice and Bob outcomes whenever some spin observable is measured at both sites. We prove that, for all states from this class, the maximal violation of the original Bell inequality is upper bounded by 3 2 and specify the two-qubit states where this quantum upper bound is attained. The case of two-qutrit states is more complicated. Here, for all two-qutrit states, we obtain the same upper bound 3 2 for violation of the original Bell inequality under Alice and Bob spin measurements, but we have not yet been able to show that this quantum upper bound is the least one. We discuss experimental consequences of our mathematical study.

scholarly journals Bell’s inequality, generalized concurrence and entanglement in qubits

2019 ◽  
Vol 34 (06n07) ◽  
pp. 1950032 ◽  
Author(s):  
Po-Yao Chang ◽  
Su-Kuan Chu ◽  
Chen-Te Ma
Keyword(s):  
Upper Bound ◽  
Entanglement Entropy ◽  
Qubit State ◽  
Bell’S Inequality ◽  
Bell's Inequality ◽  
Qubit System ◽  
Maximal Violation ◽  
Topological Entanglement Entropy ◽  
Qubit States

It is well known that the maximal violation of the Bell’s inequality for a two-qubit system is related to the entanglement formation in terms of a concurrence. However, a generalization of this relation to an [Formula: see text]-qubit state has not been found. In this paper, we demonstrate some extensions of the relation between the upper bound of the Bell’s violation and a generalized concurrence in several [Formula: see text]-qubit states. In particular, we show the upper bound of the Bell’s violation can be expressed as a function of the generalized concurrence, if a state can be expressed in terms of two variables. We apply the relation to the Wen-Plaquette model and show that the topological entanglement entropy can be extracted from the maximal Bell’s violation.

scholarly journals Progress on Quantum Discord of Two-Qubit States: Optimization and Upper Bound

2014 ◽  
Vol 54 (1) ◽  
pp. 72-84 ◽  
Author(s):  
S. Javad Akhtarshenas ◽  
Hamidreza Mohammadi ◽  
Fahimeh S. Mousavi ◽  
Vahid Nassajpour
Keyword(s):  
Upper Bound ◽  
Quantum Discord ◽  
Qubit States

ABSENCE OF A GAP IN THE EXCITATION SPECTRUM (PHONONS) OF ANHARMONIC SOLIDS

1987 ◽  
Vol 01 (01n02) ◽  
pp. 1-5 ◽  
Author(s):  
DANIEL C. MATTIS
Keyword(s):  
Excitation Spectrum ◽  
Speed Of Sound ◽  
Upper Bound ◽  
Ground State ◽  
General Class ◽  
Normal Modes ◽  
Quantum Limit ◽  
Elastic Solids ◽  
Elementary Excitations ◽  
Molecular Solid

Acoustic phonons are the suitably quantized low-lying normal modes of elastic solids. Their energies ε(k) are given by ε(k)=ħω(k), where the frequencies ω(k) are proportional to k (k=wavevector, or inverse wavelength) and vanish as w=sk (s=speed of sound) in the limit k→0. Here we prove a similar result for a reasonably general class of anharmonic solids, applicable even to such solids as the various He4 phases, H2 molecular solid, etc., which are in the extreme quantum limit. We show that the spectrum of elementary excitations in the harmonic solid provides an upper bound to the spectrum of elementary excitations in the similar anharmonic solid having the same ground state interatomic spring constantsK.

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.

Optimization of coherent attacks in generalizations of the BB84 quantum bit commitment protocol

2002 ◽  
Vol 2 (1) ◽  
pp. 66-96
Author(s):  
R.W. Spekkens ◽  
T. Rudolph
Keyword(s):  
State Estimation ◽  
Quantum State ◽  
Upper Bound ◽  
Upper Bounds ◽  
Entangled State ◽  
Quantum State Estimation ◽  
Quantum Bit ◽  
Bit Commitment ◽  
Single Qubit ◽  
Qubit States

It is well known that no quantum bit commitment protocol is unconditionally secure. Nonetheless, there can be non-trivial upper bounds on both Bob's probability of correctly estimating Alice's commitment and Alice's probability of successfully unveiling whatever bit she desires. In this paper, we seek to determine these bounds for generalizations of the BB84 bit commitment protocol. In such protocols, an honest Alice commits to a bit by randomly choosing a state from a specified set and submitting this to Bob, and later unveils the bit to Bob by announcing the chosen state, at which point Bob measures the projector onto the state. Bob's optimal cheating strategy can be easily deduced from well known results in the theory of quantum state estimation. We show how to understand Alice's most general cheating strategy, (which involves her submitting to Bob one half of an entangled state) in terms of a theorem of Hughston, Jozsa and Wootters. We also show how the problem of optimizing Alice's cheating strategy for a fixed submitted state can be mapped onto a problem of state estimation. Finally, using the Bloch ball representation of qubit states, we identify the optimal coherent attack for a class of protocols that can be implemented with just a single qubit. These results provide a tight upper bound on Alice's probability of successfully unveiling whatever bit she desires in the protocol proposed by Aharonov et al., and lead us to identify a qubit protocol with even greater security.

scholarly journals On the existence of a local quasi hidden variable (LqHV) model for each N-qudit state and the maximal quantum violation of Bell inequalities

2016 ◽  
Vol 14 (04) ◽  
pp. 1640010 ◽  
Author(s):  
Elena R. Loubenets
Keyword(s):  
Upper Bound ◽  
Probability Model ◽  
Bell Inequalities ◽  
Text Setting ◽  
Von Neumann ◽  
Hidden Variable ◽  
Probabilistic Description ◽  
Local Probability ◽  
Maximal Violation ◽  
Joint Probabilities

We specify the local quasi hidden variable (LqHV) model reproducing the probabilistic description of all N-partite joint von Neumann measurements on an N-qudit state. Via this local probability model, we derive a new upper bound on the maximal violation by an N-qudit state of Bell inequalities of any type (either on correlation functions or on joint probabilities) for [Formula: see text] observables per site. This new upper bound not only improves for all [Formula: see text] [Formula: see text] and d the corresponding results available for general Bell inequalities in the literature but also, for the N-qubit case with two observables per site, reduces exactly to the attainable upper bound known for quantum violations of correlation [Formula: see text] setting Bell inequalities in a dichotomic case.

Bipartite Bell Inequality and Maximal Violation

2011 ◽  
Vol 55 (3) ◽  
pp. 418-420 ◽  
Author(s):  
Ming Li ◽  
Shao-Ming Fei ◽  
Xian-Qing Li-Jost
Keyword(s):  
Bell Inequality ◽  
Maximal Violation
Sign in / Sign up

Export Citation Format

Share Document