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 Quantum Mechanics Interpretation on Planck Scale

2020 ◽  
Vol 65 (1) ◽  
pp. 17
Author(s):  
I. Licata
Keyword(s):  
Quantum Mechanics ◽  
Standard Model ◽  
Particle Physics ◽  
Planck Scale ◽  
Beyond The Standard Model ◽  
Interpretation Of Quantum Mechanics ◽  
Vacuum Model ◽  
The Standard Model ◽  
Local Correlations ◽  
Non Local

In the last years, many different primeval quantization theories on the Planck scale have been developed. Their goal is to provide a vacuum model able to ground the research beyond the Standard Model. Despite their goal is quite ambitious and aims toward particle physics, a necessary and notable consequence is we can read Quantum Mechanics from an emergent viewpoint. Different hypotheses on elementary cells are possible. We will focus here on the conceptual features of G. ’t Hooft and F.Winterberg theories with a special attention for the emerging of non-local correlations. These theories define a new style in the interpretation of Quantum Mechanics.

scholarly journals Tsirelson's bound and supersymmetric entangled states

2014 ◽  
Vol 470 (2170) ◽  
pp. 20140253 ◽  
Author(s):  
L. Borsten ◽  
K. Brádler ◽  
M. J. Duff
Keyword(s):  
Hilbert Space ◽  
Quantum Mechanics ◽  
Transition Probabilities ◽  
Entangled States ◽  
Supersymmetric Extension ◽  
Standard Quantum ◽  
Local Resource ◽  
Non Local ◽  
Minimal Supersymmetric Extension ◽  
Tsirelson Bound

A superqubit, belonging to a (2|1)-dimensional super-Hilbert space, constitutes the minimal supersymmetric extension of the conventional qubit. In order to see whether superqubits are more non-local than ordinary qubits, we construct a class of two-superqubit entangled states as a non-local resource in the CHSH game. Since super Hilbert space amplitudes are Grassmann numbers, the result depends on how we extract real probabilities and we examine three choices of map: (1) DeWitt (2) Trigonometric and (3) Modified Rogers. In cases (1) and (2), the winning probability reaches the Tsirelson bound p win = cos 2 π / 8 ≃ 0.8536 of standard quantum mechanics. Case (3) crosses Tsirelson's bound with p win ≃0.9265. Although all states used in the game involve probabilities lying between 0 and 1, case (3) permits other changes of basis inducing negative transition probabilities.

scholarly journals CORRELATIONS IN ENTANGLED STATES

2006 ◽  
Vol 20 (11n13) ◽  
pp. 1496-1503
Author(s):  
B. C. SANCTUARY
Keyword(s):  
Quantum Mechanics ◽  
Singlet State ◽  
Entangled States ◽  
Quantum Mechanical ◽  
Interpretation Of Quantum Mechanics ◽  
Hidden Variable ◽  
Phase Decoherence ◽  
Classical Correlations ◽  
Spin Pairs ◽  
Ensemble Interpretation

Entangled EPR spin pairs can be treated using the statistical ensemble interpretation of quantum mechanics. As such the singlet state results from an ensemble of spin pairs each with its own specific axis of quantization. This axis acts like a quantum mechanical hidden variable. If the spins lose coherence they disentangle into a mixed state that contains classical correlations. In this paper an infinitesimal phase decoherence is introduced to the singlet state in order to reveal more clearly some of the correlations. It is shown that a singlet state has no classical correlations.

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 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 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.

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