scholarly journals Some trends and problems in quantum probability

1984 ◽  
pp. 1-19 ◽  
Author(s):  
Luigi Accardi
Keyword(s):  
Quantum Probability

Quantum Probability Calculus as Fuzzy-Kolmogorovian Probability Calculus

2009 ◽  
Author(s):  
Jarosław Pykacz ◽  
Luigi Accardi ◽  
Guillaume Adenier ◽  
Christopher Fuchs ◽  
Gregg Jaeger ◽  
...  
Keyword(s):  
Quantum Probability ◽  
Probability Calculus

SPIN-PARITY EFFECT IN VIOLATION OF BELL'S INEQUALITIES

2013 ◽  
Vol 28 (01) ◽  
pp. 1450004 ◽  
Author(s):  
ZHIGANG SONG ◽  
J.-Q. LIANG ◽  
L.-F. WEI
Keyword(s):  
Berry Phase ◽  
Quantum Probability ◽  
Quantum Nonlocality ◽  
Entangled State ◽  
Bell’S Inequalities ◽  
Bipartite Entanglement ◽  
Spin Parity ◽  
Parity Effect ◽  
Bell's Inequalities ◽  
Spin Parity Effect

Analytic formulas of Bell correlations are derived in terms of quantum probability statistics under the assumption of measuring outcome-independence and the Bell's inequalities (BIs) are extended to general bipartite-entanglement macroscopic quantum-states (MQS) of arbitrary spins. For a spin-½ entangled state we find analytically that the violations of BIs really resulted from the quantum nonlocal correlations. However, the BIs are always satisfied for the spin-1 entangled MQS. More generally the quantum nonlocality does not lead to the violation for the integer spins since the nonlocal interference effects cancel each other by the quantum statistical-average. Such a cancellation no longer exists for the half-integer spins due to the nontrivial Berry phase, and thus the violation of BIs is understood remarkably as an effect of geometric phase. Specifically, our generic observation of the spin-parity effect can be experimentally tested with the entangled photon-pairs.

scholarly journals Quantum probability in decision making from quantum information representation of neuronal states

2018 ◽  
Vol 8 (1) ◽  
Author(s):  
Andrei Khrennikov ◽  
Irina Basieva ◽  
Emmanuel M. Pothos ◽  
Ichiro Yamato
Keyword(s):  
Decision Making ◽  
Quantum Information ◽  
Quantum Probability ◽  
Information Representation

scholarly journals Testing Quantum Coherence in Stochastic Electrodynamics with Squeezed Schrödinger Cat States

Atoms ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 42 ◽  
Author(s):  
Wayne Huang ◽  
Herman Batelaan
Keyword(s):  
Quantum Mechanics ◽  
Probability Distribution ◽  
Interference Pattern ◽  
Quantum Coherence ◽  
Laser Pulses ◽  
Quantum Probability ◽  
Harmonic Oscillators ◽  
Stochastic Electrodynamics ◽  
Schrödinger Cat ◽  
Cat States

The interference pattern in electron double-slit diffraction is a hallmark of quantum mechanics. A long-standing question for stochastic electrodynamics (SED) is whether or not it is capable of reproducing such effects, as interference is a manifestation of quantum coherence. In this study, we used excited harmonic oscillators to directly test this quantum feature in SED. We used two counter-propagating dichromatic laser pulses to promote a ground-state harmonic oscillator to a squeezed Schrödinger cat state. Upon recombination of the two well-separated wavepackets, an interference pattern emerges in the quantum probability distribution but is absent in the SED probability distribution. We thus give a counterexample that rejects SED as a valid alternative to quantum mechanics.

scholarly journals A quantum probabilistic approach to Hecke algebras for 𝔭-adic PGL2

2018 ◽  
Vol 21 (03) ◽  
pp. 1850015
Author(s):  
Takehiro Hasegawa ◽  
Hayato Saigo ◽  
Seiken Saito ◽  
Shingo Sugiyama
Keyword(s):  
Inversion Formula ◽  
Probabilistic Approach ◽  
Hecke Algebras ◽  
Hecke Algebra ◽  
Quantum Probability ◽  
Probabilistic Interpretation ◽  
Fourier Inversion ◽  
Fourier Inversion Formula ◽  
The Subject

The subject of the present paper is an application of quantum probability to [Formula: see text]-adic objects. We give a quantum-probabilistic interpretation of the spherical Hecke algebra for [Formula: see text], where [Formula: see text] is a [Formula: see text]-adic field. As a byproduct, we obtain a new proof of the Fourier inversion formula for [Formula: see text].

scholarly journals Curved Interference Pattern Created by Photons Behaving as Particle---Double Slit Experiment Still Has Much to Offer

2021 ◽  
Author(s):  
Hui Peng
Keyword(s):  
Interference Pattern ◽  
Wave Theory ◽  
Quantum Probability ◽  
The Novel ◽  
Physics First ◽  
Airy Beam ◽  
Comprehensive Information ◽  
Classical Wave ◽  
Double Slit Experiment ◽  
Double Slit

Abstract Young’s double slit experiments, which represent the mystery of quantum mechanics, have been described by either the classical wave, or quantum probability waves or pilot waves. Recently, the novel experiments show that the interference patterns of the double slit/cross-double slit experiments may be curved. The previous phenomena of the light bending contain the gravity bending and Airy beam curving transversely. The curved Airy beam is interpreted by the quantum Schrödinger’s wave equation and electromagnetic wave theory. To study the curved interference patterns of the comprehensive double slit experiments, we study the underlying physics first, namely, to study whether the light beam/photons behave as wave or as particle before forming the curved interference pattern. In this article, the comprehensive double slit experiments are performed, which show: (1) the fringes of the curved interference pattern are created independently and may be create partially; (2) the longitudinal shield and the metal tube inserted between the slide and the detector has no effect on the interference pattern. The experimental observations suggest that, before forming the curved interference pattern on the detector, photons behave as particles, which can be referred as “wave-particle-coexistence”. The phenomena provide the comprehensive information/data for the theoretical study.

Sign in / Sign up

Export Citation Format

Share Document