scholarly journals Discrimination of Non-Local Correlations

Entropy ◽  
2019 ◽  
Vol 21 (2) ◽  
pp. 104 ◽  
Author(s):  
Alberto Montina ◽  
Stefan Wolf
Keyword(s):  
Communication Complexity ◽  
Simple Algorithm ◽  
Running Time ◽  
Numerical Tests ◽  
Quantum Non Locality ◽  
Local Correlations ◽  
Non Local ◽  
Np Complete ◽  
Very High ◽  
Non Locality

In view of the importance of quantum non-locality in cryptography, quantum computation, and communication complexity, it is crucial to decide whether a given correlation exhibits non-locality or not. As proved by Pitowski, this problem is NP-complete, and is thus computationally intractable unless NP is equal to P. In this paper, we first prove that the Euclidean distance of given correlations from the local polytope can be computed in polynomial time with arbitrary fixed error, granted the access to a certain oracle; namely, given a fixed error, we derive two upper bounds on the running time. The first bound is linear in the number of measurements. The second bound scales with the number of measurements to the sixth power. The former holds only for a very high number of measurements, and is never observed in the performed numerical tests. We, then, introduce a simple algorithm for simulating the oracle. In all of the considered numerical tests, the simulation of the oracle contributes with a multiplicative factor to the overall running time and, thus, does not affect the sixth-power law of the oracle-assisted algorithm.

scholarly journals Branching Space-Times

2021 ◽  
Author(s):  
Nuel Belnap ◽  
Thomas Müller ◽  
Tomasz Placek
Keyword(s):  
Single Case ◽  
Formal Analysis ◽  
Rigorous Theory ◽  
Quantum Non Locality ◽  
Foundations Of Physics ◽  
Local Contexts ◽  
Rigorous Framework ◽  
Non Local ◽  
Spatio Temporal ◽  
Non Locality

This book develops a rigorous theory of indeterminism as a local and modal concept. Its crucial insight is that our world contains events or processes with alternative, really possible outcomes. The theory aims at clarifying what this assumption involves, and it does it in two ways. First, it provides a mathematically rigorous framework for local and modal indeterminism. Second, we support that theory by spelling out the philosophically relevant consequences of this formulation and by showing its fruitful applications in metaphysics. To this end, we offer a formal analysis of modal correlations and of causation, which is applicable in indeterministic and non-local contexts as well. We also propose a rigorous theory of objective single-case probabilities, intended to represent degrees of possibility. In a third step, we link our theory to current physics, investigating how local and modal indeterminism relates to issues in the foundations of physics, in particular, quantum non-locality and spatio-temporal relativity. The book also ventures into the philosophy of time, showing how the theory’s resources can be used to explicate the dynamic concept of the past, present, and future based on local indeterminism.

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.

Water-Related Mechanisms Proposed for Storing and Transmitting Homeopathic Information: Putative Links with Biological Responses

Homeopathy ◽  
2018 ◽  
Vol 107 (03) ◽  
pp. 172-180 ◽  
Author(s):  
Leoni Bonamin ◽  
Vera Capelozzi ◽  
José Guedes
Keyword(s):  
Electric Resonance ◽  
Atomic Structures ◽  
Cellular Effects ◽  
Biological Responses ◽  
Quantum Non Locality ◽  
Key Points ◽  
Scientific Approach ◽  
Non Local ◽  
Transfer Of Information ◽  
Non Locality

Introduction There are two critical pillars of homeopathy that contrast with the dominant scientific approach: the similitude principle and the potentization of serial dilutions. Three main hypotheses about the mechanisms of action are in discussion: nanobubbles-related hormesis; vehicle-related electric resonance; and quantum non-locality. Objectives The aim of this paper is to review and discuss some key points of such properties: the imprint of supramolecular structures based on the nanoparticle-allostatic, cross-adaptation-sensitization (NPCAS) model; the theory of non-molecular electromagnetic transfer of information, based on the coherent water domains model, and relying (like the NPCAS model) on the idea of local interactions; and the hypothesis of quantum entanglement, based on the concept of non-locality. Results and Discussion The nanoparticles hypothesis has been considered since 2010, after the demonstration of suspended metal nanoparticles even in very highly diluted remedies: their actual action on biological structures is still under scrutiny. The second hypothesis considers the idea of electric resonance mechanisms between living systems (including intracellular water) and homeopathic medicines: recent findings about potency-related physical properties corroborate it. Finally, quantum theory of ‘non-local’ phenomena inspires the idea of an ‘entanglement’ process among patient, practitioner and the remedy: that quantic phenomena could occur in supra-atomic structures remains speculative however. Conclusion Further studies are needed to ascertain whether and which of these hypotheses may be related to potential cellular effects of homeopathic preparations, such as organization of metabolic pathways or selective gene expression.

scholarly journals Implications of superstrong non-locality for cryptography

2006 ◽  
Vol 462 (2071) ◽  
pp. 1919-1932 ◽  
Author(s):  
Harry Buhrman ◽  
Matthias Christandl ◽  
Falk Unger ◽  
Stephanie Wehner ◽  
Andreas Winter
Keyword(s):  
Quantum Mechanics ◽  
Oblivious Transfer ◽  
Secure Computation ◽  
Bit Commitment ◽  
Local Correlations ◽  
Non Local ◽  
Non Locality

Non-local boxes are hypothetical ‘machines’ that give rise to superstrong non-local correlations, leading to a stronger violation of Bell/Clauser, Horne, Shimony & Holt inequalities than is possible within the framework of quantum mechanics. We show how non-local boxes can be used to perform any two-party secure computation. We first construct a protocol for bit commitment and then show how to achieve oblivious transfer using non-local boxes. Both have been shown to be impossible using quantum mechanics alone.

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.

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.

scholarly journals Randomness and Non-Locality

2016 ◽  
Vol 15 (03) ◽  
pp. 1640005 ◽  
Author(s):  
Gabriel Senno ◽  
Ariel Bendersky ◽  
Santiago Figueira
Keyword(s):  
Quantum Information ◽  
Information Science ◽  
Quantum Information Science ◽  
Recent Advances ◽  
Local Correlations ◽  
Distant Measurement ◽  
Non Local ◽  
Non Locality

The concepts of randomness and non-locality are intimately intertwined outcomes of randomly chosen measurements over entangled systems exhibiting non-local correlations are, if we preclude instantaneous influence between distant measurement choices and outcomes, random. In this paper, we survey some recent advances in the knowledge of the interplay between these two important notions from a quantum information science perspective.

Quantum Becoming?

2017 ◽  
Author(s):  
Craig Callender
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Quantum Time ◽  
Quantum Non Locality ◽  
Time Quantum ◽  
Temporal Becoming ◽  
Non Locality ◽  
Quantum Wavefunction

Two of quantum mechanics’ more famed and spooky features have been invoked in defending the idea that quantum time is congenial to manifest time. Quantum non-locality is said by some to make a preferred foliation of spacetime necessary, and the collapse of the quantum wavefunction is held to vindicate temporal becoming. Although many philosophers and physicists seek relief from relativity’s assault on time in quantum theory, assistance is not so easily found.

scholarly journals Evaluating probabilistic forecasts of football matches: the case against the ranked probability score

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Edward Wheatcroft
Keyword(s):  
Scoring Rules ◽  
Brier Score ◽  
Sporting Events ◽  
Forecast Performance ◽  
Scoring Rule ◽  
Probability Score ◽  
Probabilistic Forecasts ◽  
Non Local ◽  
Evaluating Forecasts ◽  
Non Locality

Abstract A scoring rule is a function of a probabilistic forecast and a corresponding outcome used to evaluate forecast performance. There is some debate as to which scoring rules are most appropriate for evaluating forecasts of sporting events. This paper focuses on forecasts of the outcomes of football matches. The ranked probability score (RPS) is often recommended since it is ‘sensitive to distance’, that is it takes into account the ordering in the outcomes (a home win is ‘closer’ to a draw than it is to an away win). In this paper, this reasoning is disputed on the basis that it adds nothing in terms of the usual aims of using scoring rules. A local scoring rule is one that only takes the probability placed on the outcome into consideration. Two simulation experiments are carried out to compare the performance of the RPS, which is non-local and sensitive to distance, the Brier score, which is non-local and insensitive to distance, and the Ignorance score, which is local and insensitive to distance. The Ignorance score outperforms both the RPS and the Brier score, casting doubt on the value of non-locality and sensitivity to distance as properties of scoring rules in this context.

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