Operational Quantum Frames: An operational approach to quantum reference frames

• URL: http://arxiv.org/abs/2304.07021v2
• Date: Sun, 3 Sep 2023 11:26:18 GMT
• Title: Operational Quantum Frames: An operational approach to quantum reference frames
• Authors: Jan G{\l}owacki
• Abstract summary: We introduce an operational notion of a quantum reference frame -- which is defined as a quantum system equipped with a covariant positive operator-valued measure (POVM) We show that when the frame is localizable, meaning that it allows for states that give rise to a highly localized probability distribution of the frame's observable, by restricting the relative description upon such localized frame preparation we recover the usual, non-relational formalism of quantum mechanics.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The quantum reference frames program is based on the idea that reference frames should be treated as quantum physical systems. In this work, we combine these insights with the emphasis on operationality, understood as refraining from introducing into the framework objects not directly related to in principle verifiable probabilities of measurement outcomes, and identifying the setups indistinguishable as such. Based on intuitions from special relativity and gauge theory, we introduce an operational notion of a quantum reference frame -- which is defined as a quantum system equipped with a covariant positive operator-valued measure (POVM) -- and build a framework on the concept of operational equivalence that allows us to enforce operationality by quotienting the quantum state spaces with equivalence relation of indistinguishability by the available effects, assumed to be invariant under gauge transformations, and framed in the sense of respecting the choice of the frame's POVM. Such effects are accessed via the yen construction, which maps effects on the system to those on the composite system, satisfying gauge invariance and framing. They are called relative, and the classes of states indistinguishable by them are referred to as relative states. We show that when the frame is localizable, meaning that it allows for states that give rise to a highly localized probability distribution of the frame's observable, by restricting the relative description upon such localized frame preparation we recover the usual, non-relational formalism of quantum mechanics. We provide a consistent way of translating between different relative descriptions by means of frame-change maps and compare these with the corresponding notions in other approaches to QRF, establishing an operational agreement in the domain of common applicability.

Related papers

• Equivalence Relations in Quantum Theory: An Objective Account of Bases and Factorizations [0.0]
  In orthodox Standard Quantum Mechanics (SQM) bases and factorizations are considered to define quantum states and entanglement in relativistic terms. We provide an invariant account of bases and factorizations which allows us to build a conceptual-operational bridge between formalism and quantum phenomena.
  arXiv  Detail & Related papers  (2024-04-23T10:17:49Z)
• Relativization is naturally functorial [0.0]
  We provide some categorical perspectives on the relativization construction arising from quantum measurement theory. This construction provides, for any quantum system, a quantum channel from the system's algebra to the invariant algebra on the composite system.
  arXiv  Detail & Related papers  (2024-03-06T14:42:22Z)
• Sufficient condition for universal quantum computation using bosonic circuits [44.99833362998488]
  We focus on promoting circuits that are otherwise simulatable to computational universality. We first introduce a general framework for mapping a continuous-variable state into a qubit state. We then cast existing maps into this framework, including the modular and stabilizer subsystem decompositions.
  arXiv  Detail & Related papers  (2023-09-14T16:15:14Z)
• Measurement events relative to temporal quantum reference frames [44.99833362998488]
  We compare two consistent approaches to the Page-Wootters formalism to clarify the operational meaning of evolution and measurements. We show that for non-ideal clocks, the purified measurement approach yields time non-local, non-unitary evolution.
  arXiv  Detail & Related papers  (2023-08-21T18:26:12Z)
• Operational Quantum Reference Frame Transformations [0.0]
  We provide a general, operationally motivated framework for quantum reference frames and their transformations. The work is built around the notion of operational equivalence, in which quantum states that cannot be physically distinguished are identified. We give an explicit realisation in the setting that the initial frame admits a highly localized state with respect to the frame observable.
  arXiv  Detail & Related papers  (2023-03-24T13:58:21Z)
• Quantum Reference Frames on Finite Homogeneous Spaces [0.0]
  We focus on the case that the reference observable is the canonical covariant projection valued measure on the given space. We show that this gives rise to a rank-one covariant POVM on the group, which can be seen as a system of coherent states.
  arXiv  Detail & Related papers  (2023-02-10T16:16:18Z)
• Quantum state inference from coarse-grained descriptions: analysis and an application to quantum thermodynamics [101.18253437732933]
  We compare the Maximum Entropy Principle method, with the recently proposed Average Assignment Map method. Despite the fact that the assigned descriptions respect the measured constraints, the descriptions differ in scenarios that go beyond the traditional system-environment structure.
  arXiv  Detail & Related papers  (2022-05-16T19:42:24Z)
• Effective descriptions of localization in a proper-time parametrized framework [0.0]
  We show the connection between proper-time formalism and usual descriptions parametrized by classical observers. We retrieve the concepts of Newton-Wigner position and Kijowski time of detection.
  arXiv  Detail & Related papers  (2021-07-24T13:04:04Z)
• Quantum indistinguishability through exchangeable desirable gambles [69.62715388742298]
  Two particles are identical if all their intrinsic properties, such as spin and charge, are the same. Quantum mechanics is seen as a normative and algorithmic theory guiding an agent to assess her subjective beliefs represented as (coherent) sets of gambles. We show how sets of exchangeable observables (gambles) may be updated after a measurement and discuss the issue of defining entanglement for indistinguishable particle systems.
  arXiv  Detail & Related papers  (2021-05-10T13:11:59Z)
• Quantum Relativity of Subsystems [58.720142291102135]
  We show that different reference frame perspectives induce different sets of subsystem observable algebras, which leads to a gauge-invariant, frame-dependent notion of subsystems and entanglement. Such a QRF perspective does not inherit the distinction between subsystems in terms of the corresponding tensor factorizability of the kinematical Hilbert space and observable algebra. Since the condition for this to occur is contingent on the choice of QRF, the notion of subsystem locality is frame-dependent.
  arXiv  Detail & Related papers  (2021-03-01T19:00:01Z)
• Equivalence of approaches to relational quantum dynamics in relativistic settings [68.8204255655161]
  We show that the trinity' of relational quantum dynamics holds in relativistic settings per frequency superselection sector. We ascribe the time according to the clock subsystem to a POVM which is covariant with respect to its (quadratic) Hamiltonian.
  arXiv  Detail & Related papers  (2020-07-01T16:12:24Z)

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.