Local sampling of the SU(1,1) Wigner function

• URL: http://arxiv.org/abs/2301.08127v1
• Date: Thu, 19 Jan 2023 15:46:28 GMT
• Title: Local sampling of the SU(1,1) Wigner function
• Abstract summary: We capitalize on the unique properties of the parity operator, to derive in a consistent way a Wigner function that faithfully parallels the structure of its continuous-variable counterpart. We propose an optical scheme, involving a squeezer and photon-number-resolving detectors, that allows for direct point-by-point sampling of that Wigner function.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: Despite the indisputable merits of the Wigner phase-space formulation, it has not been widely explored for systems with SU(1,1) symmetry, as a simple operational definition of the Wigner function has proved elusive in this case. We capitalize on the unique properties of the parity operator, to derive in a consistent way a \emph{bona fide} SU(1,1) Wigner function that faithfully parallels the structure of its continuous-variable counterpart. We propose an optical scheme, involving a squeezer and photon-number-resolving detectors, that allows for direct point-by-point sampling of that Wigner function. This provides an adequate framework to represent SU(1,1) states satisfactorily.

Related papers

• Wigner negativity and stellar rank for SU(1,1) states [0.43496401697112685]
  Quasiprobability distributions for systems endowed with SU (1,1) dynamical symmetry are studied.<n>We show that the Wigner function is strictly positive for all Perelomov SU (1,1) coherent states.<n>We also examine the stellar rank of SU (1,1) states, defined through the zeros of the Husimi $Q$-function.
  arXiv  Detail & Related papers  (2026-07-24T18:00:00Z)
• High-accuracy log-concave sampling with stochastic queries [70.90863485771405]
  We show that high-accuracy guarantees for log-concave sampling are achievable using iteration gradients with subexponential tails.<n>Our framework also provides similar high accuracy guarantees under zeroth order (value) queries.
  arXiv  Detail & Related papers  (2026-02-15T23:19:07Z)
• Wigner entropy conjecture and the interference formula in quantum phase space [0.0]
  Wigner-positive quantum states have the peculiarity to admit a Wigner function that is a genuine probability distribution over phase space. We prove that this Wigner entropy conjecture holds true for a broad class of Wigner-positive states known as beam-splitter states.
  arXiv  Detail & Related papers  (2024-11-08T13:37:05Z)
• Sample Complexity for Quadratic Bandits: Hessian Dependent Bounds and Optimal Algorithms [64.10576998630981]
  We show the first tight characterization of the optimal Hessian-dependent sample complexity. A Hessian-independent algorithm universally achieves the optimal sample complexities for all Hessian instances. The optimal sample complexities achieved by our algorithm remain valid for heavy-tailed noise distributions.
  arXiv  Detail & Related papers  (2023-06-21T17:03:22Z)
• Sub-Planck phase-space structure and sensitivity for SU(1,1) compass states [0.0]
  We show that the Planck scale on the hyperbolic plane can be considered as the inverse of the Bargmann index $k$. Superpositions of four Perelomov SU (1,1) coherent states (compass state) yield nearly isotropic sub-Planck structures in phase space scaling.
  arXiv  Detail & Related papers  (2022-07-26T07:50:30Z)
• Reinforcement Learning from Partial Observation: Linear Function Approximation with Provable Sample Efficiency [111.83670279016599]
  We study reinforcement learning for partially observed decision processes (POMDPs) with infinite observation and state spaces. We make the first attempt at partial observability and function approximation for a class of POMDPs with a linear structure.
  arXiv  Detail & Related papers  (2022-04-20T21:15:38Z)
• Energy transitions driven by phase space reflection operators [0.0]
  Phase space reflection operators lie at the core of the Wigner-Weyl representation of density operators and observables. In their active role as unitary operators, they generate transitions between pairs of eigenstates specified by Wigner functions. It is shown here how the improved approximation of the spectral Wigner functions in terms of Airy functions resolves the singularity.
  arXiv  Detail & Related papers  (2022-01-05T20:46:00Z)
• Sinkhorn Natural Gradient for Generative Models [125.89871274202439]
  We propose a novel Sinkhorn Natural Gradient (SiNG) algorithm which acts as a steepest descent method on the probability space endowed with the Sinkhorn divergence. We show that the Sinkhorn information matrix (SIM), a key component of SiNG, has an explicit expression and can be evaluated accurately in complexity that scales logarithmically. In our experiments, we quantitatively compare SiNG with state-of-the-art SGD-type solvers on generative tasks to demonstrate its efficiency and efficacy of our method.
  arXiv  Detail & Related papers  (2020-11-09T02:51:17Z)
• Kenfack Zyczkowski indicator of nonclassicality for two non-equivalent representations of Wigner function of qutrit [0.0]
  Wigner function of a finite-dimensional system can be constructed via dual pairing of a density matrix with the Stratonovich-Weyl kernel. We consider the indicator of nonclassicality of a finite-dimensional quantum system which depends on the volume of the negative part of the Wigner function.
  arXiv  Detail & Related papers  (2020-09-01T12:11:29Z)
• Random extrapolation for primal-dual coordinate descent [61.55967255151027]
  We introduce a randomly extrapolated primal-dual coordinate descent method that adapts to sparsity of the data matrix and the favorable structures of the objective function. We show almost sure convergence of the sequence and optimal sublinear convergence rates for the primal-dual gap and objective values, in the general convex-concave case.
  arXiv  Detail & Related papers  (2020-07-13T17:39:35Z)
• Infinite Feature Selection: A Graph-based Feature Filtering Approach [78.63188057505012]
  We propose a filtering feature selection framework that considers subsets of features as paths in a graph. Going to infinite allows to constrain the computational complexity of the selection process. We show that Inf-FS behaves better in almost any situation, that is, when the number of features to keep are fixed a priori.
  arXiv  Detail & Related papers  (2020-06-15T07:20:40Z)
• Formal Synthesis of Lyapunov Neural Networks [61.79595926825511]
  We propose an automatic and formally sound method for synthesising Lyapunov functions. We employ a counterexample-guided approach where a numerical learner and a symbolic verifier interact to construct provably correct Lyapunov neural networks. Our method synthesises Lyapunov functions faster and over wider spatial domains than the alternatives, yet providing stronger or equal guarantees.
  arXiv  Detail & Related papers  (2020-03-19T17:21:02Z)
• Efficient Quantum Tomography of Two-Mode Wigner Functions [0.0]
  We introduce an efficient method to reconstruct the Wigner function of many-mode continuous variable systems. A key ingredient of the proposed approach is the representation of the state in a truncated Fock basis.
  arXiv  Detail & Related papers  (2019-12-27T16:29:40Z)

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.