Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Mathematical Physics

A definition of quantum detection point processes

Christine Bénard

Published Mar 1, 1975• 2 citations
Publisher

Abstract

A definition of quantum particle detection point processes is given for normal and locally normal systems. This is realized by building coincidence measurement operators, describing in a thoroughly quantum formalism the coincidence experiments that have been actually performed (photon) or that might be performed (electron, neutron). The quantum mean values of these coincidence operators are shown to be the coincidence probabilities of a mathematically well−defined regular process. Some applications of the latter result are given, in particular in the case of fermion point processes.

DOI
10.1063/1.522586

Related papers

Fluctuations of Beams of Quantum Particles

Christine Bénard

A beam of noninteracting particles, bosons or fermions, is described by the superposition of stochastic wave packets. This description allows in each case (bosons or fermions) the determination of the detection process of the particles. This process is defined by the set of the $p$-order coincidence probability densities, a general formulation of which is given. In the case of a stationary and weak incoherent beam, these coincidence probability densities are studied thoroughly and several results are obtained. The well-known bunching effect for bosons and the "antibunching effect" for fermions are shown to come from the detection of indistinguishable particles. In the boson case, all the well-known results for thermal light are found. In the fermion case, the detection process is, under certain conditions, identical to a renewal process.

Physical Review A•Nov 1, 1970•14 citations

Quantum counting processes

M. D. Srinivas

It is proposed that counting experiments in quantum physics should be analyzed in terms of point processes (QPP) defined in the framework of quantum probability theory. A coincidence approach is developed for a class QPP called the regular QPP. A counting formula is derived which determines completely the counting statistics of a regular QPP by means of a pair of ’’generators.’’

Journal of Mathematical Physics•Nov 1, 1977•30 citations

QUANTUM PROBABILITIES FROM DETECTION THEORY FOR CLASSICAL RANDOM FIELD

Andrei Yu. Khrennikov

We present a model of detectors operating with classical random fields and producing probabilities described by the formalism of quantum mechanics. The basic assumption of this measurement theory is that the probability of detection of field (= signal) is proportional to the power of this field. (Therefore we call this approach "power signal-field detection theory" – PFSDT.) Our approach has some similarities with stochastic electrodynamics. However, formalisms describing random fields – "quantum fluctuations" – are different. Moreover, our approach all particles are represented by random fields, e.g., electronic or neutronic field. Thus we have various types of "quantum fluctuations".

Fluctuation and Noise Letters•Dec 1, 2008•4 citations

Detection and ``emission'' processes of quantum particles in a ``chaotic state''

Christine Bénard, Odile Macchi

We study the statistical properties of a chaotic beam of quantum particles (bosons or fermions) by using wavepacket formalism, which allows us to deal with bosons and fermions in a very symmetrical way. Our study is based on the definition and analysis of two different stochastic point processes consisting, respectively, of the ``emission'' time instants and detection time instants (or positions in a space) of the particles of the beam. The two processes are shown to be identical in the chaotic boson case and in the chaotic fermion case, respectively. The symmetry between the well-known results concerning the photon detection process and the new results concerning the fermion detection process is pointed out. And finally it is noted that in the chaotic case the bunching (or antibunching) effect is present already in the ``emission'' of the particles.

Journal of Mathematical Physics•Feb 1, 1973•22 citations

Physical Meaning of the Optimum Measurement Process in Quantum Detection Theory

Masao Osaki, Haruhisa Kozuka, Osamu Hirota

The optimum measurement processes are represented as the optimum detection operators in the quantum detection theory. The error probability by the optimum detection operators goes beyond the standard quantum limit automatically. However the optimum detection operators are given by pure mathematical descriptions. In order to realize a communication system overcoming the standard quantum limit, we try to give the physical meaning of the optimum detection operators.

•Jan 1, 1996•1 citation

Classical signal model reproducing quantum probabilities for single and coincidence detections

Andrei Yu. Khrennikov, Börje Nilsson, Sven Nordebo

We present a simple classical (random) signal model reproducing Born's rule. The crucial point of our approach is that the presence of detector's threshold and calibration procedure have to be treated not as simply experimental technicalities, but as the basic counterparts of the theoretical model. We call this approach threshold signal detection model (TSD). The experiment on coincidence detection which was done by Grangier in 1986 [22] played a crucial role in rejection of (semi-)classical field models in favour of quantum mechanics (QM): impossibility to resolve the wave-particle duality in favour of a purely wave model. QM predicts that the relative probability of coincidence detection, the coefficient g (2) (0), is zero (for one photon states), but in (semi-)classical models g (2) (0) ≥ 1. In TSD the coefficient g (2) (0) decreases as 1/ ε 2 d , where ε d > 0 is the detection threshold. Hence, by increasing this threshold an experimenter can make the coefficient g (2) (0) essentially less than 1. The TSD-prediction can be tested experimentally in new Grangier type experiments presenting a detailed monitoring of dependence of the coefficient g (2) (0) on the detection threshold. Structurally our model has some similarity with the prequantum model of Grossing et al. Subquantum stochasticity is composed of the two counterparts: a stationary process in the space of internal degrees of freedom and the random walk type motion describing the temporal dynamics.

arXiv:1112.5591•Journal of Physics Conference Series•May 10, 2012•14 citations
A definition of quantum particle detection point processes is given for normal and locally normal systems. This is realized by building coincidence measurement operators, describing in a thoroughly quantum formalism the coincidence experiments that have been actually performed (photon) or that might be performed (electron, neutron). The quantum mean values of these coincidence operators are shown to be the coincidence probabilities of a mathematically well−defined regular process. Some applications of the latter result are given, in particular in the case of fermion point processes.
A beam of noninteracting particles, bosons or fermions, is described by the superposition of stochastic wave packets. This description allows in each case (bosons or fermions) the determination of the detection process of the particles. This process is defined by the set of the ppp-order coincidence probability densities, a general formulation of which is given. In the case of a stationary and weak incoherent beam, these coincidence probability densities are studied thoroughly and several results are obtained. The well-known bunching effect for bosons and the "antibunching effect" for fermions are shown to come from the detection of indistinguishable particles. In the boson case, all the well-known results for thermal light are found. In the fermion case, the detection process is, under certain conditions, identical to a renewal process.
We present a model of detectors operating with classical random fields and producing probabilities described by the formalism of quantum mechanics. The basic assumption of this measurement theory is that the probability of detection of field (= signal) is proportional to the power of this field. (Therefore we call this approach "power signal-field detection theory" – PFSDT.) Our approach has some similarities with stochastic electrodynamics. However, formalisms describing random fields – "quantum fluctuations" – are different. Moreover, our approach all particles are represented by random fields, e.g., electronic or neutronic field. Thus we have various types of "quantum fluctuations".
We study the statistical properties of a chaotic beam of quantum particles (bosons or fermions) by using wavepacket formalism, which allows us to deal with bosons and fermions in a very symmetrical way. Our study is based on the definition and analysis of two different stochastic point processes consisting, respectively, of the ``emission'' time instants and detection time instants (or positions in a space) of the particles of the beam. The two processes are shown to be identical in the chaotic boson case and in the chaotic fermion case, respectively. The symmetry between the well-known results concerning the photon detection process and the new results concerning the fermion detection process is pointed out. And finally it is noted that in the chaotic case the bunching (or antibunching) effect is present already in the ``emission'' of the particles.
We present a simple classical (random) signal model reproducing Born's rule. The crucial point of our approach is that the presence of detector's threshold and calibration procedure have to be treated not as simply experimental technicalities, but as the basic counterparts of the theoretical model. We call this approach threshold signal detection model (TSD). The experiment on coincidence detection which was done by Grangier in 1986 [22] played a crucial role in rejection of (semi-)classical field models in favour of quantum mechanics (QM): impossibility to resolve the wave-particle duality in favour of a purely wave model. QM predicts that the relative probability of coincidence detection, the coefficient g (2) (0), is zero (for one photon states), but in (semi-)classical models g (2) (0) ≥ 1. In TSD the coefficient g (2) (0) decreases as 1/ ε 2 d , where ε d > 0 is the detection threshold. Hence, by increasing this threshold an experimenter can make the coefficient g (2) (0) essentially less than 1. The TSD-prediction can be tested experimentally in new Grangier type experiments presenting a detailed monitoring of dependence of the coefficient g (2) (0) on the detection threshold. Structurally our model has some similarity with the prequantum model of Grossing et al. Subquantum stochasticity is composed of the two counterparts: a stationary process in the space of internal degrees of freedom and the random walk type motion describing the temporal dynamics.