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.

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.

THOUGHTS ON NON-LOCALITY AND QUANTUM MECHANICS

2006 ◽  
Vol 04 (01) ◽  
pp. 209-218 ◽  
Author(s):  
W. UNRUH
Keyword(s):  
Quantum Mechanics ◽  
20Th Century ◽  
Additional Assumption ◽  
Hidden Variables ◽  
Late 20Th Century ◽  
Hardy Type ◽  
Non Local ◽  
The Difference ◽  
Numerous People ◽  
Non Locality

The debate about the non-locality of quantum mechanics is old, but still lively. Numerous people use non-locality as (bad) shorthand for quantum entanglement. But some have a long-standing commitment to the validity of this characterization. This paper examines two separate streams in this debate. The first is the arguments of Stapp, and especially his recent paper where he simplifies his contractual argument in the Hardy situation to argue for the non-locality of quantum mechanics. He has maintained his contention that an analysis of a Hardy-type correlation between two spatially separated observers proves that quantum mechanics itself is non-local, without any additional assumption of realism or hidden variables. In the second section, I try to carefully examine the Bell argument in the CHSH variant to see where the difference between the quantum and classical situations differ. Asher Peres was one of the great physicists of the late 20th century, especially for his intense concern with the fundamental nature of quantum mechanics. His courage in devoting his life to an area many considered "philosophical" (i.e. non-physical) paved the way for the rest of us to reveal our interests and confusions about this area. I am not sure that he would agree with everything in this paper, but I offer it as a tribute to him.

scholarly journals Relaxed uncertainty relations and information processing

2009 ◽  
Vol 9 (9&10) ◽  
pp. 801-832 ◽  
Author(s):  
G. Ver Steeg ◽  
S. Wehner
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Uncertainty Relation ◽  
Random Access ◽  
The Other ◽  
Uncertainty Relations ◽  
Expectation Values ◽  
Chsh Inequality ◽  
Local Correlations ◽  
Non Local

We consider a range of "theories'' that violate the uncertainty relation for anti-commuting observables derived. We first show that Tsirelson's bound for the CHSH inequality can be derived from this uncertainty relation, and that relaxing this relation allows for non-local correlations that are stronger than what can be obtained in quantum mechanics. We continue to construct a hierarchy of related non-signaling theories, and show that on one hand they admit superstrong random access encodings and exponential savings for a particular communication problem, while on the other hand it becomes much harder in these theories to learn a state. We show that the existence of these effects stems from the absence of certain constraints on the expectation values of commuting measurements from our non-signaling theories that are present in quantum theory.

scholarly journals On quantum entanglement, counterfactuals, causality and dispositions

Synthese ◽  
2017 ◽  
Vol 197 (10) ◽  
pp. 4161-4185
Author(s):  
Tomasz Bigaj
Keyword(s):  
Quantum Mechanics ◽  
Entangled States ◽  
Causal Mechanism ◽  
Interpretation Of Quantum Mechanics ◽  
Counterfactual Conditionals ◽  
Local Character ◽  
Causal Connections ◽  
Local Correlations ◽  
Non Local ◽  
Counterfactual Approach

Abstract The existence of non-local correlations between outcomes of measurements in quantum entangled systems strongly suggests that we are dealing with some form of causation here. An assessment of this conjecture in the context of the collapse interpretation of quantum mechanics is the primary goal of this paper. Following the counterfactual approach to causation, I argue that the details of the underlying causal mechanism which could explain the non-local correlations in entangled states strongly depend on the adopted semantics for counterfactuals. Several relativistically-invariant interpretations of spatiotemporal counterfactual conditionals are discussed, and the corresponding causal stories describing interactions between parts of an entangled system are evaluated. It is observed that the most controversial feature of the postulated causal connections is not so much their non-local character as a peculiar type of circularity that affects them.

scholarly journals NON-LOCALITY OF QUANTUM MECHANICS AND THE LOCALITY OF GENERAL RELATIVITY

2002 ◽  
Vol 17 (15n17) ◽  
pp. 1097-1106 ◽  
Author(s):  
JEEVA ANANDAN
Keyword(s):  
General Relativity ◽  
Quantum Mechanics ◽  
Gauge Fields ◽  
Abelian Gauge ◽  
Non Local ◽  
Frame Work ◽  
Time Description ◽  
Aharonov Bohm ◽  
Space Description ◽  
Non Locality

The conflict between the locality of general relativity, reflected in its space-time description, and the non-locality of quantum mechanics, contained in its Hilbert space description, is discussed. Gauge covariant non-local observables that depend on gauge fields and gravity as well as the wave function are used in order to try to understand and minimize this conflict within the frame-work of these two theories. Applications are made to the Aharonov-Bohm effect and its generalizations to non Abelian gauge fields and gravity.

scholarly journals The Operational Choi–Jamiołkowski Isomorphism

Entropy ◽  
2020 ◽  
Vol 22 (9) ◽  
pp. 1063 ◽  
Author(s):  
Emily Adlam
Keyword(s):  
Quantum Mechanics ◽  
Causal Structure ◽  
Temporal Correlations ◽  
Fundamental Object ◽  
Generalized Probabilistic Theories ◽  
Operational Theory ◽  
Local Correlations ◽  
Non Local ◽  
Operational Formulation ◽  
Probabilistic Theories

In this article, I use an operational formulation of the Choi–Jamiołkowski isomorphism to explore an approach to quantum mechanics in which the state is not the fundamental object. I first situate this project in the context of generalized probabilistic theories and argue that this framework may be understood as a means of drawing conclusions about the intratheoretic causal structure of quantum mechanics which are independent of any specific ontological picture. I then give an operational formulation of the Choi–Jamiołkowski isomorphism and show that, in an operational theory which exhibits this isomorphism, several features of the theory which are usually regarded as properties of the quantum state can be derived from constraints on non-local correlations. This demonstrates that there is no need to postulate states to be the bearers of these properties, since they can be understood as consequences of a fundamental equivalence between multipartite and temporal correlations.

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 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.

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