From point processes to quantum optics and back

• URL: http://arxiv.org/abs/2210.05522v1
• Date: Tue, 11 Oct 2022 15:15:04 GMT
• Title: From point processes to quantum optics and back
• Authors: R\'emi Bardenet, Alexandre Feller, J\'er\'emie Bouttier, Pascal Degiovanni, Adrien Hardy, Adam Ran\c{c}on, Benjamin Roussel, Gr\'egory Schehr and Christoph I. Westbrook
• Abstract summary: Some fifty years ago, in her seminal PhD thesis, Odile Macchi introduced permanental and determinantal point processes. These point processes have quickly become standard examples of point processes with nontrivial, yet tractable, correlation structures. Our objective is to provide a shared basis of knowledge for later cross-disciplinary work on point processes in quantum optics.
• Score: 49.5703193576447
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Some fifty years ago, in her seminal PhD thesis, Odile Macchi introduced permanental and determinantal point processes. Her initial motivation was to provide models for the set of detection times in fundamental bosonic or fermionic optical experiments, respectively. After two rather quiet decades, these point processes have quickly become standard examples of point processes with nontrivial, yet tractable, correlation structures. In particular, determinantal point processes have been since the 1990s a technical workhorse in random matrix theory and combinatorics, and a standard model for repulsive point patterns in machine learning and spatial statistics since the 2010s. Meanwhile, our ability to experimentally probe the correlations between detection events in bosonic and fermionic optics has progressed tremendously. In Part I of this survey, we provide a modern introduction to the concepts in Macchi's thesis and their physical motivation, under the combined eye of mathematicians, physicists, and signal processers. Our objective is to provide a shared basis of knowledge for later cross-disciplinary work on point processes in quantum optics, and reconnect with the physical roots of permanental and determinantal point processes.

Related papers

• Dephasing in the central spin problem with long-range Ising spin-bath coupling [0.0]
  We study the central limit theorem of qubit dephasing in the central spin model. We prove this approximation for a bath depicted by an Ising spin system. We show that in certain cases, namely for short-range (exponentially decaying) coupling, this approximation breaks.
  arXiv  Detail & Related papers  (2024-09-19T13:14:31Z)
• Many-time physics in practice: characterising and controlling non-Markovian quantum stochastic processes [0.0]
  We present a generalisation of quantum process tomography, called process tensor tomography (PTT) PTT establishes the ability to rigorously and systematically non-Markovian open quantum systems. We develop the framework of PTT, including experiment design, post-processing algorithms, and both simulated and near-term device demonstrations.
  arXiv  Detail & Related papers  (2024-05-08T20:34:53Z)
• The time crystal phase emerges from the qubit network under unitary random operations [9.793615002494237]
  We report findings of non-stationary behavior observed in a fully connected qubit network. Our research provides a new perspective for constructing the time crystal phase in an open system model.
  arXiv  Detail & Related papers  (2023-04-06T06:26:38Z)
• A Quantum-Classical Model of Brain Dynamics [62.997667081978825]
  Mixed Weyl symbol is used to describe brain processes at the microscopic level. Electromagnetic fields and phonon modes involved in the processes are treated either classically or semi-classically. Zero-point quantum effects can be incorporated into numerical simulations by controlling the temperature of each field mode.
  arXiv  Detail & Related papers  (2023-01-17T15:16:21Z)
• Geometric phases along quantum trajectories [58.720142291102135]
  We study the distribution function of geometric phases in monitored quantum systems. For the single trajectory exhibiting no quantum jumps, a topological transition in the phase acquired after a cycle. For the same parameters, the density matrix does not show any interference.
  arXiv  Detail & Related papers  (2023-01-10T22:05:18Z)
• The Quantum Path Kernel: a Generalized Quantum Neural Tangent Kernel for Deep Quantum Machine Learning [52.77024349608834]
  Building a quantum analog of classical deep neural networks represents a fundamental challenge in quantum computing. Key issue is how to address the inherent non-linearity of classical deep learning. We introduce the Quantum Path Kernel, a formulation of quantum machine learning capable of replicating those aspects of deep machine learning.
  arXiv  Detail & Related papers  (2022-12-22T16:06:24Z)
• Learning quantum processes without input control [2.6089354079273512]
  We introduce a general statistical learning theory for processes that take as input a classical random variable and output a quantum state. This framework is applicable to the study of astronomical phenomena, disordered systems and biological processes not controlled by the observer.
  arXiv  Detail & Related papers  (2022-11-09T16:34:46Z)
• DriPP: Driven Point Processes to Model Stimuli Induced Patterns in M/EEG Signals [62.997667081978825]
  We develop a novel statistical point process model-called driven temporal point processes (DriPP) We derive a fast and principled expectation-maximization (EM) algorithm to estimate the parameters of this model. Results on standard MEG datasets demonstrate that our methodology reveals event-related neural responses.
  arXiv  Detail & Related papers  (2021-12-08T13:07:21Z)
• From many-body to many-time physics [0.0]
  Multi-time quantum processes endowed with the same richness as many-body physics. We show how surprisingly accessible, yet under-explored, these phenomena are in nascent quantum processors.
  arXiv  Detail & Related papers  (2021-07-29T12:48:10Z)
• Discovering Latent Causal Variables via Mechanism Sparsity: A New Principle for Nonlinear ICA [81.4991350761909]
  Independent component analysis (ICA) refers to an ensemble of methods which formalize this goal and provide estimation procedure for practical application. We show that the latent variables can be recovered up to a permutation if one regularizes the latent mechanisms to be sparse.
  arXiv  Detail & Related papers  (2021-07-21T14:22:14Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.