Measurement of a quantum system with a classical apparatus using ensembles on configuration space

• URL: http://arxiv.org/abs/2205.09632v1
• Date: Thu, 19 May 2022 15:48:12 GMT
• Title: Measurement of a quantum system with a classical apparatus using ensembles on configuration space
• Authors: Marcel Reginatto and Sebastian Ulbricht
• Abstract summary: We use the approach of ensembles on configurations space to give a detailed account of a classical apparatus measuring the position of a quantum particle. We show that the probability of the pointer of the classical apparatus is left in a state that corresponds to the probability of the quantum particle. Since this formalism incorporates uncertainties and finite measurement precision, it is well suited for metrological applications.
• Score: 0.48733623015338234
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Finding a physically consistent approach to modelling interactions between classical and quantum systems is a highly nontrivial task. While many proposals based on various mathematical formalisms have been made, most of these efforts run into difficulties of one sort or another. One of the first detailed descriptions was given by Sudarshan and his collaborators who, motivated by the measurement problem in quantum mechanics, proposed a Hilbert space formulation of classical-quantum interactions which made use of the Koopman-von Neumann description of classical systems. Here we use the approach of ensembles on configurations space to give a detailed account of a classical apparatus measuring the position of a quantum particle that is prepared in a superposition of two localized states. We show that the probability of the pointer of the classical apparatus is left in a state that corresponds to the probability of the quantum particle. A subsequent observation of the pointer leads to an update of its probability density. From this we can obtain information about the position of the quantum particle, leading to an update of its wave function. Since this formalism incorporates uncertainties and finite measurement precision, it is well suited for metrological applications. Furthermore, it resolves fundamental issues that appear in the case of a quantum description of the apparatus.

Related papers

• To be or not to be, but where? [0.0]
  Traditional approaches associate quantum systems with classical ones localized in spacetime. canonical linearized quantum gravity disrupts this framework by preventing the formation of gauge-in-variant local algebras. This presents a major obstacle for modeling early universe cosmology, gravity-entanglement experiments, and poses a significant roadblock toward a comprehensive theory of quantum gravity.
  arXiv  Detail & Related papers  (2024-05-31T17:22:39Z)
• Ergodic and chaotic properties in Tavis-Cummings dimer: quantum and classical limit [0.0]
  We investigate two key aspects of quantum systems by using the Tavis-Cummings dimer system as a platform. The first aspect involves unraveling the relationship between the phenomenon of self-trapping (or lack thereof) and integrability (or quantum chaos) Secondly, we uncover the possibility of mixed behavior in this quantum system using diagnostics based on random matrix theory.
  arXiv  Detail & Related papers  (2024-04-21T13:05:29Z)
• Markovian dynamics for a quantum/classical system and quantum trajectories [0.0]
  We develop a general approach to the dynamics of quantum/classical systems. An important feature is that, if the interaction allows for a flow of information from the quantum component to the classical one, necessarily the dynamics is dissipative.
  arXiv  Detail & Related papers  (2024-03-24T08:26:54Z)
• Does the system entanglement care about the readout efficiency of quantum measurement? [49.1574468325115]
  We quantify the entanglement for a particle on a 1d quantum random walk under inefficient monitoring. We find that the system's maximal mean entanglement at the measurement-induced quantum-to-classical crossover is in different ways by the measurement strength and inefficiency.
  arXiv  Detail & Related papers  (2024-02-29T18:10:05Z)
• Quantum data learning for quantum simulations in high-energy physics [55.41644538483948]
  We explore the applicability of quantum-data learning to practical problems in high-energy physics. We make use of ansatz based on quantum convolutional neural networks and numerically show that it is capable of recognizing quantum phases of ground states. The observation of non-trivial learning properties demonstrated in these benchmarks will motivate further exploration of the quantum-data learning architecture in high-energy physics.
  arXiv  Detail & Related papers  (2023-06-29T18:00:01Z)
• Relational superposition measurements with a material quantum ruler [2.912552849396905]
  We introduce a model to describe an extended material quantum system working as a position measurement device. We show that we can define a quantum measurement procedure corresponding to the "superposition of positions" The model is fully relational, because the only meaningful variables are the relative positions between the ruler and the system.
  arXiv  Detail & Related papers  (2023-06-01T05:03:21Z)
• Anticipative measurements in hybrid quantum-classical computation [68.8204255655161]
  We present an approach where the quantum computation is supplemented by a classical result. Taking advantage of its anticipation also leads to a new type of quantum measurements, which we call anticipative. In an anticipative quantum measurement the combination of the results from classical and quantum computations happens only in the end.
  arXiv  Detail & Related papers  (2022-09-12T15:47:44Z)
• Quantum tomography explains quantum mechanics [0.0]
  A suggestive notion for what constitutes a quantum detector leads to a logically impeccable definition of measurement. The various forms of quantum tomography for quantum states, quantum detectors, quantum processes, and quantum instruments are discussed. The new approach is closer to actual practice than the traditional foundations.
  arXiv  Detail & Related papers  (2021-10-11T14:09:30Z)
• From geometry to coherent dissipative dynamics in quantum mechanics [68.8204255655161]
  We work out the case of finite-level systems, for which it is shown by means of the corresponding contact master equation. We describe quantum decays in a 2-level system as coherent and continuous processes.
  arXiv  Detail & Related papers  (2021-07-29T18:27:38Z)
• Preparing random states and benchmarking with many-body quantum chaos [48.044162981804526]
  We show how to predict and experimentally observe the emergence of random state ensembles naturally under time-independent Hamiltonian dynamics. The observed random ensembles emerge from projective measurements and are intimately linked to universal correlations built up between subsystems of a larger quantum system. Our work has implications for understanding randomness in quantum dynamics, and enables applications of this concept in a wider context.
  arXiv  Detail & Related papers  (2021-03-05T08:32:43Z)
• From a quantum theory to a classical one [117.44028458220427]
  We present and discuss a formal approach for describing the quantum to classical crossover. The method was originally introduced by L. Yaffe in 1982 for tackling large-$N$ quantum field theories.
  arXiv  Detail & Related papers  (2020-04-01T09:16:38Z)

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.