The group structure of dynamical transformations between quantum reference frames

• URL: http://arxiv.org/abs/2012.15769v2
• Date: Fri, 7 May 2021 21:48:58 GMT
• Title: The group structure of dynamical transformations between quantum reference frames
• Authors: Angel Ballesteros, Flaminia Giacomini, Giulia Gubitosi
• Abstract summary: 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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Recently, it was shown that when reference frames are associated to quantum systems, the transformation laws between such quantum reference frames need to be modified to take into account the quantum and dynamical features of the reference frames. This led to a relational description of the phase space variables of the quantum system of which the quantum reference frames are part of. While such transformations were shown to be symmetries of the system's Hamiltonian, the question remained unanswered as to whether they enjoy a group structure, similar to that of the Galilei group relating classical reference frames in quantum mechanics. In this work, we identify the canonical transformations on the phase space of the quantum systems comprising the quantum reference frames, and show that these transformations close a group structure defined by a Lie algebra, which is different from the usual Galilei algebra of quantum mechanics. We further find that the elements of this new algebra are in fact the building blocks of the quantum reference frames transformations previously identified, which we recover. Finally, we show how the transformations between classical reference frames described by the standard Galilei group symmetries can be obtained from the group of transformations between quantum reference frames by taking the zero limit of the parameter that governs the additional noncommutativity introduced by the quantum nature of inertial transformations.

Related papers

• 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)
• On reconstruction of states from evolution induced by quantum dynamical semigroups perturbed by covariant measures [50.24983453990065]
  We show the ability to restore states of quantum systems from evolution induced by quantum dynamical semigroups perturbed by covariant measures. Our procedure describes reconstruction of quantum states transmitted via quantum channels and as a particular example can be applied to reconstruction of photonic states transmitted via optical fibers.
  arXiv  Detail & Related papers  (2023-12-02T09:56:00Z)
• Quantifying measurement-induced quantum-to-classical crossover using an open-system entanglement measure [49.1574468325115]
  We study the entanglement of a single particle under continuous measurements. We find that the entanglement at intermediate time scales shows the same qualitative behavior as a function of the measurement strength.
  arXiv  Detail & Related papers  (2023-04-06T09:45:11Z)
• Quantum Frames of Reference and the Noncommutative Values of Observables [0.0]
  We show how the value' of an observable for a fixed state change can be translated. The essence of the quantum reference frame transformations is to have the quantum fluctuations, and even entanglement, of the physical object taken into account.
  arXiv  Detail & Related papers  (2021-12-06T04:37:56Z)
• Relative subsystems and quantum reference frame transformations [0.0]
  We derive quantum reference frame transformations from first principles, using only standard quantum theory. We find more general transformations than those studied so far, which are valid only in a restricted subspace. Our framework contains additional degrees of freedom in the form of an "extra particle," which carries information about the quantum features of reference frame states.
  arXiv  Detail & Related papers  (2021-10-25T18:23:28Z)
• 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)
• Transformation of Spin in Quantum Reference Frames [0.0]
  We develop a framework for rotational (i.e. spin) quantum reference frames. This is the first development of the quantum reference frame formalism for a non-Abelian group.
  arXiv  Detail & Related papers  (2021-03-08T19:09:23Z)
• 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)
• 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)
• Unraveling the topology of dissipative quantum systems [58.720142291102135]
  We discuss topology in dissipative quantum systems from the perspective of quantum trajectories. We show for a broad family of translation-invariant collapse models that the set of dark state-inducing Hamiltonians imposes a nontrivial topological structure on the space of Hamiltonians.
  arXiv  Detail & Related papers  (2020-07-12T11:26:02Z)
• 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.