Quantum Reference Frames from Top-Down Crossed Products

• URL: http://arxiv.org/abs/2405.13884v2
• Date: Mon, 1 Jul 2024 19:01:33 GMT
• Title: Quantum Reference Frames from Top-Down Crossed Products
• Authors: Shadi Ali Ahmad, Wissam Chemissany, Marc S. Klinger, Robert G. Leigh,
• Abstract summary: Crossed product is a way to realize quantum reference frames from the bottom-up. We show that one cannot obtain in quantumequivalent reference frames using this approach. We term this algebra the G-framed algebra, and show how potentially inequivalent frames are realized within this object.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: All physical observations are made relative to a reference frame, which is a system in its own right. If the system of interest admits a group symmetry, the reference frame observing it must transform commensurately under the group to ensure the covariance of the combined system. We point out that the crossed product is a way to realize quantum reference frames from the bottom-up; adjoining a quantum reference frame and imposing constraints generates a crossed product algebra. We provide a top-down specification of crossed product algebras and show that one cannot obtain inequivalent quantum reference frames using this approach. As a remedy, we define an abstract algebra associated to the system and symmetry group built out of relational crossed product algebras associated with different choices of quantum reference frames. We term this object the G-framed algebra, and show how potentially inequivalent frames are realized within this object. We comment on this algebra's analog of the classical Gribov problem in gauge theory, its importance in gravity where we show that it is relevant for semiclassical de Sitter and potentially beyond the semiclassical limit, and its utility for understanding the frame-dependence of physical notions like observables, density states, and entropies.

Related papers

• Geometric Quantum Machine Learning with Horizontal Quantum Gates [41.912613724593875]
  We propose an alternative paradigm for the symmetry-informed construction of variational quantum circuits. We achieve this by introducing horizontal quantum gates, which only transform the state with respect to the directions to those of the symmetry. For a particular subclass of horizontal gates based on symmetric spaces, we can obtain efficient circuit decompositions for our gates through the KAK theorem.
  arXiv  Detail & Related papers  (2024-06-06T18:04:39Z)
• 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)
• Matter relative to quantum hypersurfaces [44.99833362998488]
  We extend the Page-Wootters formalism to quantum field theory. By treating hypersurfaces as quantum reference frames, we extend quantum frame transformations to changes between classical and nonclassical hypersurfaces.
  arXiv  Detail & Related papers  (2023-08-24T16:39:00Z)
• Fermionic anyons: entanglement and quantum computation from a resource-theoretic perspective [39.58317527488534]
  We develop a framework to characterize the separability of a specific type of one-dimensional quasiparticle known as a fermionic anyon. We map this notion of fermionic-anyon separability to the free resources of matchgate circuits. We also identify how entanglement between two qubits encoded in a dual-rail manner, as standard for matchgate circuits, corresponds to the notion of entanglement between fermionic anyons.
  arXiv  Detail & Related papers  (2023-06-01T15:25:19Z)
• 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 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)
• The group structure of dynamical transformations between quantum reference frames [0.0]
  We identify the canonical transformations on the phase space of the quantum systems comprising the quantum reference frames. We show that these transformations close a group structure defined by a Lie algebra, which is different from the usual Galilei algebra of quantum mechanics.
  arXiv  Detail & Related papers  (2020-12-31T17:42:13Z)
• Quantum particle across Grushin singularity [77.34726150561087]
  We study the phenomenon of transmission across the singularity that separates the two half-cylinders. All the local realisations of the free (Laplace-Beltrami) quantum Hamiltonian are examined as non-equivalent protocols of transmission/reflection. This allows to comprehend the distinguished status of the so-called bridging' transmission protocol previously identified in the literature.
  arXiv  Detail & Related papers  (2020-11-27T12:53:23Z)
• Quantum reference frames for general symmetry groups [0.0]
  We introduce a relational formalism which identifies coordinate systems with elements of a symmetry group $G$. This generalises the known operator for translations and boosts to arbitrary finite groups, including non-Abelian groups. We prove a theorem stating that the change of quantum reference frame consistent with these principles is unitary if and only if the reference systems carry the left and right regular representations of $G$.
  arXiv  Detail & Related papers  (2020-04-29T16:16:53Z)

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.