Connecting Commutativity and Classicality for Multi-Time Quantum Processes

• URL: http://arxiv.org/abs/2204.11698v2
• Date: Fri, 26 Aug 2022 09:24:52 GMT
• Title: Connecting Commutativity and Classicality for Multi-Time Quantum Processes
• Authors: Fattah Sakuldee, Philip Taranto, and Simon Milz
• Abstract summary: We focus on the relationship between Kolmogorov consistency of measurement statistics and the commutativity of measurement operators. On the other hand, commutativity of measurement operators is a structural property that holds in classical physics. We detail their implications for memoryless multi-time quantum processes.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Understanding the demarcation line between classical and quantum is an important issue in modern physics. The development of such an understanding requires a clear picture of the various concurrent notions of `classicality' in quantum theory presently in use. Here, we focus on the relationship between Kolmogorov consistency of measurement statistics -- the foundational footing of classical stochastic processes in standard probability theory -- and the commutativity (or absence thereof) of measurement operators -- a concept at the core of quantum theory. Kolmogorov consistency implies that the statistics of sequential measurements on a (possibly quantum) system could be explained entirely by means of a classical stochastic process, thereby providing an operational notion of classicality. On the other hand, commutativity of measurement operators is a structural property that holds in classical physics and its breakdown is the origin of the uncertainty principle, a fundamentally quantum phenomenon. Here, we formalise the connection between these two a priori independent notions of classicality, demonstrate that they are distinct in general and detail their implications for memoryless multi-time quantum processes.

Related papers

• 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)
• Relaxation of first-class constraints and the quantization of gauge theories: from "matter without matter" to the reappearance of time in quantum gravity [72.27323884094953]
  We make a conceptual overview of an approach to the initial-value problem in canonical gauge theories. We stress how the first-class phase-space constraints may be relaxed if we interpret them as fixing the values of new degrees of freedom.
  arXiv  Detail & Related papers  (2024-02-19T19:00:02Z)
• Classicality with(out) decoherence: Concepts, relation to Markovianity, and a random matrix theory approach [0.0]
  decoherence in open quantum systems, consistent/decoherent histories and Kolmogorov consistency are compared. The crucial role of quantum Markovianity (defined rigorously) to connect these concepts is established. Quantum effects are shown to be exponentially suppressed in the measurement statistics of slow and coarse observables.
  arXiv  Detail & Related papers  (2023-01-06T15:22:47Z)
• Correspondence Between the Energy Equipartition Theorem in Classical Mechanics and its Phase-Space Formulation in Quantum Mechanics [62.997667081978825]
  In quantum mechanics, the energy per degree of freedom is not equally distributed. We show that in the high-temperature regime, the classical result is recovered.
  arXiv  Detail & Related papers  (2022-05-24T20:51:03Z)
• Joint quantum-classical Hamilton variation principle in the phase space [0.0]
  We show that the dynamics of a closed quantum system obeys the Hamilton variation principle. By introducing the classical counterpart of the Husimi representation in a close analogy to the Koopman-von Neumann theory, one can largely unify the formulations of classical and quantum dynamics.
  arXiv  Detail & Related papers  (2021-11-15T06:38:08Z)
• Quantum Causal Inference in the Presence of Hidden Common Causes: an Entropic Approach [34.77250498401055]
  We put forth a new theoretical framework for merging quantum information science and causal inference by exploiting entropic principles. We apply our proposed framework to an experimentally relevant scenario of identifying message senders on quantum noisy links. This approach can lay the foundations of identifying originators of malicious activity on future multi-node quantum networks.
  arXiv  Detail & Related papers  (2021-04-24T22:45:50Z)
• Spacetime Quantum Actions [0.0]
  We propose a formulation of quantum mechanics in an extended Fock space in which a tensor product structure is applied to time. Subspaces of histories consistent with the dynamics of a particular theory are defined by a direct quantum generalization of the corresponding classical action. The diagonalization of such quantum actions enables us to recover the predictions of conventional quantum mechanics and reveals an extended unitary equivalence between all physical theories.
  arXiv  Detail & Related papers  (2020-10-18T23:14:10Z)
• Preferred basis, decoherence and a quantum state of the Universe [77.34726150561087]
  We review a number of issues in foundations of quantum theory and quantum cosmology. These issues can be considered as a part of the scientific legacy of H.D. Zeh.
  arXiv  Detail & Related papers  (2020-06-28T18:07:59Z)
• Emergence of classical behavior in the early universe [68.8204255655161]
  Three notions are often assumed to be essentially equivalent, representing different facets of the same phenomenon. We analyze them in general Friedmann-Lemaitre- Robertson-Walker space-times through the lens of geometric structures on the classical phase space. The analysis shows that: (i) inflation does not play an essential role; classical behavior can emerge much more generally; (ii) the three notions are conceptually distinct; classicality can emerge in one sense but not in another.
  arXiv  Detail & Related papers  (2020-04-22T16:38:25Z)
• 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.