Coherent representation of fields and deformation quantization

• URL: http://arxiv.org/abs/2005.14333v1
• Date: Thu, 28 May 2020 22:41:26 GMT
• Title: Coherent representation of fields and deformation quantization
• Authors: Jasel Berra-Montiel and Alberto Molgado
• Abstract summary: We explicitly consider the holomorphic representation for a scalar field within the deformation quantization program. Notably, the symbol of a symmetric ordered operator in terms of holomorphic variables may be straightforwardly obtained by the quantum field analogue of the Husimi distribution.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Motivated by some well-known results in the phase space description of quantum optics and quantum information theory, we aim to describe the formalism of quantum field theory by explicitly considering the holomorphic representation for a scalar field within the deformation quantization program. Notably, the symbol of a symmetric ordered operator in terms of holomorphic variables may be straightforwardly obtained by the quantum field analogue of the Husimi distribution associated with a normal ordered operator. This relation also allows establishing a $c$-equivalence between the Moyal and the normal star-products. In addition, by writing the density operator in terms of coherent states we are able to directly introduce a series representation of the Wigner functional distribution which may be convenient in order to calculate probability distributions of quantum field observables without performing formal phase space integrals at all.

Related papers

• 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)
• Holomorphic representation of quantum computations [0.0]
  We study bosonic quantum computations using the Segal-Bargmann representation of quantum states. We argue that this holomorphic representation is a natural one which gives a canonical description of bosonic quantum computing.
  arXiv  Detail & Related papers  (2021-10-29T23:26:51Z)
• Bosonic field digitization for quantum computers [62.997667081978825]
  We address the representation of lattice bosonic fields in a discretized field amplitude basis. We develop methods to predict error scaling and present efficient qubit implementation strategies.
  arXiv  Detail & Related papers  (2021-08-24T15:30:04Z)
• Tomography in Loop Quantum Cosmology [0.0]
  We analyze the tomographic representation for the Friedmann-Robertson-Walker (FRW) model within the Loop Quantum Cosmology framework. We focus on the Wigner quasi-probability distributions associated with Gaussian and Schr"odinger cat states.
  arXiv  Detail & Related papers  (2021-04-20T02:31:52Z)
• 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)
• Star product approach for Loop Quantum Cosmology [0.0]
  We consider the Weyl quantization map for cylindrical functions defined on the Bohr compactification of the reals. The integral representation contains all of the common properties that characterize a star product. We propose a natural way to obtain the quantum dynamical evolution in LQC in terms of this star commutator.
  arXiv  Detail & Related papers  (2020-10-17T04:02:52Z)
• Quasi-probability distributions in Loop Quantum Cosmology [0.0]
  We introduce a complete family of parametrized quasi-probability distributions in phase space and their corresponding Weyl quantization maps. We expect our results may serve to analyze several fundamental aspects within the Loop Quantum Cosmology program.
  arXiv  Detail & Related papers  (2020-07-02T18:05:32Z)
• State preparation and measurement in a quantum simulation of the O(3) sigma model [65.01359242860215]
  We show that fixed points of the non-linear O(3) sigma model can be reproduced near a quantum phase transition of a spin model with just two qubits per lattice site. We apply Trotter methods to obtain results for the complexity of adiabatic ground state preparation in both the weak-coupling and quantum-critical regimes. We present and analyze a quantum algorithm based on non-unitary randomized simulation methods.
  arXiv  Detail & Related papers  (2020-06-28T23:44:12Z)
• Deformation quantization and the tomographic representation of quantum fields [0.0]
  The tomographic representation of quantum fields within the deformation quantization formalism is constructed. Some possible applications of the formalism to loop quantum cosmology and loop quantum gravity are briefly discussed.
  arXiv  Detail & Related papers  (2020-06-13T17:43:02Z)
• Quantum Statistical Complexity Measure as a Signalling of Correlation Transitions [55.41644538483948]
  We introduce a quantum version for the statistical complexity measure, in the context of quantum information theory, and use it as a signalling function of quantum order-disorder transitions. We apply our measure to two exactly solvable Hamiltonian models, namely: the $1D$-Quantum Ising Model and the Heisenberg XXZ spin-$1/2$ chain. We also compute this measure for one-qubit and two-qubit reduced states for the considered models, and analyse its behaviour across its quantum phase transitions for finite system sizes as well as in the thermodynamic limit by using Bethe ansatz.
  arXiv  Detail & Related papers  (2020-02-05T00:45:21Z)
• Bulk detection of time-dependent topological transitions in quenched chiral models [48.7576911714538]
  We show that the winding number of the Hamiltonian eigenstates can be read-out by measuring the mean chiral displacement of a single-particle wavefunction. This implies that the mean chiral displacement can detect the winding number even when the underlying Hamiltonian is quenched between different topological phases.
  arXiv  Detail & Related papers  (2020-01-16T17:44:52Z)

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.