An anomaly of non-locality

2007 ◽  
Vol 7 (1&2) ◽  
pp. 157-170 ◽  
Author(s):  
A.A. Methot ◽  
V. Scarani
Keyword(s):  
Bell Inequalities ◽  
Present Knowledge ◽  
Quantum States ◽  
Entangled States ◽  
Low Dimensions ◽  
Local Correlations ◽  
Non Local ◽  
Entangled Quantum States ◽  
Maximally Entangled States ◽  
Non Locality

Ever since the work of Bell, it has been known that entangled quantum states can produce non-local correlations between the outcomes of separate measurements. However, for almost forty years, it has been assumed that the most non-local states would be the maximally entangled ones. Surprisingly it is not the case: non-maximally entangled states are generally more non-local than maximally entangled states for all the measures of non-locality proposed to date: Bell inequalities, the Kullback-Leibler distance, entanglement simulation with communication or with non-local boxes, the detection loophole and efficiency of cryptography. In fact, one can even find simple examples in low dimensions, confirming that it is not an artefact of a specifically constructed Hilbert space or topology. This anomaly shows that entanglement and non-locality are not only different concepts, but also truly different resources. We review the present knowledge on this anomaly, point out that Hardy's theorem has the same feature, and discuss the perspectives opened by these discoveries.

“Non-locality”

2017 ◽  
Author(s):  
Richard Healey
Keyword(s):  
Quantum Theory ◽  
Quantum Entanglement ◽  
Quantum States ◽  
Entangled States ◽  
Entangled Quantum States ◽  
Action At A Distance ◽  
Insight Into ◽  
Non Locality

Quantum entanglement is popularly believed to give rise to spooky action at a distance of a kind that Einstein decisively rejected. Indeed, important recent experiments on systems assigned entangled states have been claimed to refute Einstein by exhibiting such spooky action. After reviewing two considerations in favor of this view I argue that quantum theory can be used to explain puzzling correlations correctly predicted by assignment of entangled quantum states with no such instantaneous action at a distance. We owe both considerations in favor of the view to arguments of John Bell. I present simplified forms of these arguments as well as a game that provides insight into the situation. The argument I give in response turns on a prescriptive view of quantum states that differs both from Dirac’s (as stated in Chapter 2) and Einstein’s.

scholarly journals Non-local box complexity and secure function evaluation

2011 ◽  
Vol 11 (1&2) ◽  
pp. 40-69
Author(s):  
Marc Kaplan ◽  
Sophie Laplante ◽  
Iordanis Kerenidis ◽  
J\'er\'emie Roland
Keyword(s):  
Boolean Function ◽  
Lower Bounds ◽  
Communication Complexity ◽  
Upper And Lower Bounds ◽  
Entangled States ◽  
Function Evaluation ◽  
Secure Function Evaluation ◽  
Non Local ◽  
Maximally Entangled States ◽  
Non Locality

A non-local box is an abstract device into which Alice and Bob input bits $x$ and $y$ respectively and receive outputs $a$ and $b$, where $a,b$ are uniformly distributed and $a \oplus b = x \wedge y$. Such boxes have been central to the study of quantum or generalized non-locality, as well as the simulation of non-signaling distributions. In this paper, we start by studying how many non-local boxes Alice and Bob need in order to compute a Boolean function $f$. We provide tight upper and lower bounds in terms of the communication complexity of the function both in the deterministic and randomized case. We show that non-local box complexity has interesting applications to classical cryptography, in particular to secure function evaluation, and study the question posed by Beimel and Malkin \cite{BM} of how many Oblivious Transfer calls Alice and Bob need in order to securely compute a function $f$. We show that this question is related to the non-local box complexity of the function and conclude by greatly improving their bounds. Finally, another consequence of our results is that traceless two-outcome measurements on maximally entangled states can be simulated with 3 \nlbs, while no finite bound was previously known.

Introduction, generation and entanglement of entangled displaced even and odd squeezed states

2021 ◽  
pp. 2050047
Author(s):  
Amir Karimi
Keyword(s):  
Quantum States ◽  
Entangled States ◽  
Squeezed States ◽  
Displacement Operator ◽  
Text Type ◽  
Level Atom ◽  
Displacement Parameter ◽  
Entangled Quantum States ◽  
Quantized Field ◽  
Classical Fields

In this paper, first, we introduce special types of entangled quantum states named “entangled displaced even and odd squeezed states” by using displaced even and odd squeezed states which are constructed via the action of displacement operator on the even and odd squeezed states, respectively. Next, we present a theoretical scheme to generate the introduced entangled states. This scheme is based on the interaction between a [Formula: see text]-type three-level atom and a two-mode quantized field in the presence of two strong classical fields. In the continuation, we consider the entanglement feature of the introduced entangled states by evaluating concurrence. Moreover, we study the influence of the displacement parameter on the entanglement degree of the introduced entangled states and compare the results. It will be observed that the concurrence of the “entangled displaced odd squeezed states” has less decrement with respect to the “entangled displaced even squeezed states” by increasing the displacement parameter.

scholarly journals Quantum Correlation via Skew Information and Bell Function Beyond Entanglement in a Two-Qubit Heisenberg XYZ Model: Effect of the Phase Damping

2020 ◽  
Vol 10 (11) ◽  
pp. 3782 ◽  
Author(s):  
Abdel-Baset A. Mohamed ◽  
Ahmed Farouk ◽  
Mansour F. Yassen ◽  
Hichem Eleuch
Keyword(s):  
Sudden Change ◽  
Quantum Correlations ◽  
Physical Parameters ◽  
Phase Damping ◽  
Change Behavior ◽  
Skew Information ◽  
Local Correlations ◽  
Non Local ◽  
Moriya Interaction ◽  
Non Locality

In this paper, we analyze the dynamics of non-local correlations (NLCs) in an anisotropic two-qubit Heisenberg XYZ model under the effect of the phase damping. An analytical solution is obtained by applying a method based on the eigenstates and the eigenvalues of the Hamiltonian. It is observed that the generated NLCs are controlled by the Dzyaloshinskii–Moriya interaction, the purity indicator, the interaction with the environment, and the anisotropy. Furthermore, it is found that the quantum correlations, as well as the sudden death and sudden birth phenomena, depend on the considered physical parameters. In particular, the system presents a special correlation: the skew-information correlation. The log-negativity and the uncertainty-induced non-locality exhibit the sudden-change behavior. The purity of the initial states plays a crucial role on the generated nonlocal correlations. These correlations are sensitive to the DM interaction, anisotropy, and phase damping.

DYNAMICS OF A COUPLED CAVITY SYSTEM COMPOSED OF THREE CAVITIES

2012 ◽  
Vol 10 (06) ◽  
pp. 1250070 ◽  
Author(s):  
ZHI-RONG ZHONG ◽  
XIU LIN ◽  
BIN ZHANG ◽  
ZHEN-BIAO YANG
Keyword(s):  
Theoretical Basis ◽  
Quantum States ◽  
Entangled States ◽  
W States ◽  
Atomic Excitation ◽  
Level Atom ◽  
Cavity System ◽  
Maximally Entangled States ◽  
The One ◽  
Coupled Cavity

We study the one-excitation dynamics of a coupled cavity system composed of three cavities, each containing a two-level atom. By adjusting the atom–cavity detuning Δ, cavity–cavity hopping rate v and the initial atomic excitation residential, a wide variety of time-evolution behaviors can be realized. Under certain conditions, the two-atom maximally entangled states and three-atom W states can be obtained. The results provide a theoretical basis for the manipulation of quantum states in such a system and will contribute to the understanding of more complex systems.

scholarly journals Bell Inequalities Tailored to Maximally Entangled States

2017 ◽  
Vol 119 (4) ◽  
Author(s):  
Alexia Salavrakos ◽  
Remigiusz Augusiak ◽  
Jordi Tura ◽  
Peter Wittek ◽  
Antonio Acín ◽  
...  
Keyword(s):  
Bell Inequalities ◽  
Entangled States ◽  
Maximally Entangled States

scholarly journals Strategies for Positive Partial Transpose (PPT) States in Quantum Metrologies with Noise

Entropy ◽  
2021 ◽  
Vol 23 (6) ◽  
pp. 685
Author(s):  
Arunava Majumder ◽  
Harshank Shrotriya ◽  
Leong-Chuan Kwek
Keyword(s):  
Quantum States ◽  
Entangled States ◽  
Heisenberg Uncertainty Principle ◽  
Positive Partial Transpose ◽  
Partial Transpose ◽  
Heisenberg Uncertainty ◽  
Noise Limit ◽  
Entangled Quantum States ◽  
Standard Precision ◽  
Shot Noise Limit

Quantum metrology overcomes standard precision limits and has the potential to play a key role in quantum sensing. Quantum mechanics, through the Heisenberg uncertainty principle, imposes limits on the precision of measurements. Conventional bounds to the measurement precision such as the shot noise limit are not as fundamental as the Heisenberg limits, and can be beaten with quantum strategies that employ `quantum tricks’ such as squeezing and entanglement. Bipartite entangled quantum states with a positive partial transpose (PPT), i.e., PPT entangled states, are usually considered to be too weakly entangled for applications. Since no pure entanglement can be distilled from them, they are also called bound entangled states. We provide strategies, using which multipartite quantum states that have a positive partial transpose with respect to all bi-partitions of the particles can still outperform separable states in linear interferometers.

scholarly journals Quantum Rayleigh Annihilation of Entangled Photons

2018 ◽  
Author(s):  
Andre Vatarescu
Keyword(s):  
Physical Reality ◽  
Quantum States ◽  
Entangled States ◽  
Entangled Photons ◽  
Dielectric Media ◽  
Quantum Phenomenon ◽  
Quantum Non Locality ◽  
Linearly Polarized ◽  
Photonic States ◽  
Non Locality

The interpretation of published experimental results intended to prove the existence of a quantum phenomenon of non-locality involving photonic entangled states did not take into consideration the existence of the quantum Rayleigh conversion of photons in dielectric media. This phenomenon leads to the existence of high levels of correlations between two independent photonic and linearly polarized quantum states generated after the entangled photons have been absorbed through the quantum Rayleigh conversion. Both pure and mixed individual states of polarization result in expressions normally associated with entangled photonic states, providing support for the view that the physical reality of quantum non-locality is highly questionable.

scholarly journals Quantum Rayleigh Annihilation of Entangled Photons

2018 ◽  
Author(s):  
Andre Vatarescu
Keyword(s):  
Physical Reality ◽  
Quantum States ◽  
Entangled States ◽  
Entangled Photons ◽  
Dielectric Media ◽  
Quantum Phenomenon ◽  
Quantum Non Locality ◽  
Linearly Polarized ◽  
Photonic States ◽  
Non Locality

The interpretation of published experimental results intended to prove the existence of a quantum phenomenon of non-locality involving photonic entangled states did not take into consideration the existence of the quantum Rayleigh conversion of photons in dielectric media. This phenomenon leads to the existence of high levels of correlations between two independent photonic and linearly polarized quantum states generated after the entangled photons have been absorbed through the quantum Rayleigh conversion. Both pure and mixed individual states of polarization result in expressions normally associated with entangled photonic states, providing support for the view that the physical reality of quantum non-locality is highly questionable.

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