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.

Quantum Interference

2019 ◽  
pp. 66-88
Author(s):  
Jeffrey A. Barrett
Keyword(s):  
Hilbert Space ◽  
Wave Function ◽  
Quantum Mechanics ◽  
Quantum Interference ◽  
Standard Theory ◽  
Quantum Decoherence ◽  
Entangled States ◽  
Quantum Mechanical ◽  
Standard Formulation ◽  
Complex Valued

Moving to more subtle experiments, we consider how the standard formulation of quantum mechanics predicts and explains interference phenomena. Tracking the conditions under which one observes interference phenomena leads to the notion of quantum decoherence. We see why one must sharply distinguish between collapse phenomena and decoherence phenomena on the standard formulation of quantum mechanics. While collapses explain determinate measurement records, environmental decoherence just produces more complex, entangled states where the physical systems involved lack ordinary physical properties. We characterize the quantum-mechanical wave function as both an element of a Hilbert space and a complex-valued function over a configuration space. We also discuss how the wave function is interpreted in the standard 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 On Bell’s Inequality in PT-Symmetric Quantum Systems

2021 ◽  
Vol 3 (3) ◽  
pp. 417-424
Author(s):  
Sarang S. Bhosale ◽  
Biswanath Rath ◽  
Prasanta K. Panigrahi
Keyword(s):  
Hilbert Space ◽  
Quantum Mechanics ◽  
Quantum Systems ◽  
Inner Product ◽  
Bell’S Inequality ◽  
Standard Quantum ◽  
Bell's Inequality ◽  
Qubit System ◽  
Symmetric Quantum ◽  
No Signaling

Bell’s inequality is investigated in parity-time (PT) symmetric quantum mechanics, using a recently developed form of the inequality by Maccone [Am. J. Phys. 81, 854 (2013) ] , with two PT-qubits in the unbroken phase with real energy spectrum. It is shown that the inequality produces a bound that is consistent with the standard quantum mechanics even after using Hilbert space equipped with CPT inner product and therefore, the entanglement has identical structure with standard quantum mechanics. Consequently, the no-signaling principle for a two-qubit system in PT-symmetric quantum theory is preserved.

Nonlinear quantum mechanics in a q-deformed Hilbert space

2019 ◽  
Vol 383 (23) ◽  
pp. 2729-2738 ◽  
Author(s):  
Bruno G. da Costa ◽  
Ernesto P. Borges
Keyword(s):  
Hilbert Space ◽  
Quantum Mechanics ◽  
Nonlinear Quantum ◽  
Nonlinear Quantum Mechanics

scholarly journals Standard quantum mechanics without observers

2021 ◽  
Vol 103 (3) ◽  
Author(s):  
Ovidiu Cristinel Stoica
Keyword(s):  
Quantum Mechanics ◽  
Standard Quantum

scholarly journals Beyond Causal Explanation: Einstein’s Principle Not Reichenbach’s

Entropy ◽  
2021 ◽  
Vol 23 (1) ◽  
pp. 114
Author(s):  
Michael Silberstein ◽  
William Mark Stuckey ◽  
Timothy McDevitt
Keyword(s):  
Quantum Mechanics ◽  
Quantum Information ◽  
Causal Explanation ◽  
Causal Structure ◽  
Minkowski Spacetime ◽  
Physical Principle ◽  
Causal Principle ◽  
Complete Rejection ◽  
Epr Correlations ◽  
Tsirelson Bound

Our account provides a local, realist and fully non-causal principle explanation for EPR correlations, contextuality, no-signalling, and the Tsirelson bound. Indeed, the account herein is fully consistent with the causal structure of Minkowski spacetime. We argue that retrocausal accounts of quantum mechanics are problematic precisely because they do not fully transcend the assumption that causal or constructive explanation must always be fundamental. Unlike retrocausal accounts, our principle explanation is a complete rejection of Reichenbach’s Principle. Furthermore, we will argue that the basis for our principle account of quantum mechanics is the physical principle sought by quantum information theorists for their reconstructions of quantum mechanics. Finally, we explain why our account is both fully realist and psi-epistemic.

THE UNREASONABLE EFFECTIVENESS OF EXPONENTIALLY SUPPRESSED CORRECTIONS IN PRESERVING INFORMATION

2013 ◽  
Vol 22 (12) ◽  
pp. 1342030 ◽  
Author(s):  
KYRIAKOS PAPADODIMAS ◽  
SUVRAT RAJU
Keyword(s):  
Hilbert Space ◽  
Black Hole ◽  
Quantum Mechanics ◽  
Nonperturbative Effects ◽  
Von Neumann Entropy ◽  
Von Neumann ◽  
Information Theoretic ◽  
Black Hole Evaporation ◽  
Strong Subadditivity ◽  
Unreasonable Effectiveness

We point out that nonperturbative effects in quantum gravity are sufficient to reconcile the process of black hole evaporation with quantum mechanics. In ordinary processes, these corrections are unimportant because they are suppressed by e-S. However, they gain relevance in information-theoretic considerations because their small size is offset by the corresponding largeness of the Hilbert space. In particular, we show how such corrections can cause the von Neumann entropy of the emitted Hawking quanta to decrease after the Page time, without modifying the thermal nature of each emitted quantum. Second, we show that exponentially suppressed commutators between operators inside and outside the black hole are sufficient to resolve paradoxes associated with the strong subadditivity of entropy without any dramatic modifications of the geometry near the horizon.

scholarly journals Preparation of Entangled States through Hilbert Space Engineering

2016 ◽  
Vol 117 (14) ◽  
Author(s):  
Y. Lin ◽  
J. P. Gaebler ◽  
F. Reiter ◽  
T. R. Tan ◽  
R. Bowler ◽  
...  
Keyword(s):  
Hilbert Space ◽  
Entangled States
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