Sharp values for all dynamical variables via Anti-Wick quantization
- URL: http://arxiv.org/abs/2512.07616v1
- Date: Mon, 08 Dec 2025 15:04:54 GMT
- Title: Sharp values for all dynamical variables via Anti-Wick quantization
- Authors: Simon Friederich,
- Abstract summary: It is shown that, by using Anti-Wick quantization, quantum expectation values can be interpreted as genuine weighted averages over phase space.<n>Unlike Bohmian mechanics, the present approach retains the standard correspondence between dynamical variables and self-adjoint operators.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: This paper proposes an approach to interpreting quantum expectation values that may help address the quantum measurement problem. Quantum expectation values are usually calculated via Hilbert space inner products and, thereby, differently from expectation values in classical mechanics, which are weighted phase-space integrals. It is shown that, by using Anti-Wick quantization to associate dynamical variables with self-adjoint linear operators, quantum expectation values can be interpreted as genuine weighted averages over phase space, paralleling their classical counterparts. This interpretation arises naturally in the Segal-Bargmann space, where creation and annihilation operators act as simple multiplication and differentiation operators. In this setting, the Husimi Q-function - the coherent-state representation of the quantum state - can be seen as a true probability density in phase space. Unlike Bohmian mechanics, the present approach retains the standard correspondence between dynamical variables and self-adjoint operators while paving the way for a classical-like probabilistic interpretation of quantum statistics.
Related papers
- Experimental demonstration of generalized quantum fluctuation theorems in the presence of coherence [10.502237817201173]
We report the experimental validation of a quantum fluctuation theorem (QFT) in a photonic system.<n>Our experiment confirms that the ratio between the quasi-probabilities of the time-forward and any multiple time-reversal processes obeys a generalized Crooks QFT.<n>These findings underscore the fundamental symmetry between a general quantum process and its time reversal, providing an elementary toolkit to explore noisy quantum information processing.
arXiv Detail & Related papers (2025-05-31T12:00:59Z) - Variational Transformer Ansatz for the Density Operator of Steady States in Dissipative Quantum Many-Body Systems [44.598178952679575]
We propose the textittransformer density operator ansatz for determining the steady states of dissipative quantum many-body systems.<n>By vectorizing the density operator as a many-body state in a doubled Hilbert space, the transformer encodes the amplitude and phase of the state's coefficients.<n>We demonstrate the effectiveness of our approach by numerically calculating the steady states of dissipative Ising and Heisenberg spin chain models.
arXiv Detail & Related papers (2025-02-28T05:12:43Z) - Operationally classical simulation of quantum states [41.94295877935867]
A classical state-preparation device cannot generate superpositions and hence its emitted states must commute.<n>We show that no such simulation exists, thereby certifying quantum coherence.<n>Our approach is a possible avenue to understand how and to what extent quantum states defy generic models based on classical devices.
arXiv Detail & Related papers (2025-02-03T15:25:03Z) - Scaled quantum theory. The bouncing ball problem [0.0]
The standard bouncing ball problem is analyzed under the presence of a gravitational field and harmonic potential.
The quantum-classical transition of the density matrix is described by the linear scaled von Neumann equation for mixed states.
arXiv Detail & Related papers (2024-10-14T10:09:48Z) - Kochen-Specker non-contextuality through the lens of quantization [0.0]
The Kochen-Specker theorem shows that it is impossible to assign sharp values to all dynamical variables in quantum mechanics.
We show that for quantum theories obtained by quantizing some classical theory, this condition is implausible from the start.
Our observations suggest that the relevance of the Kochen-Specker theorem to the question of whether one can assign sharp values to all dynamical variables is rather limited.
arXiv Detail & Related papers (2024-09-19T20:10:37Z) - Variational quantum simulation using non-Gaussian continuous-variable
systems [39.58317527488534]
We present a continuous-variable variational quantum eigensolver compatible with state-of-the-art photonic technology.
The framework we introduce allows us to compare discrete and continuous variable systems without introducing a truncation of the Hilbert space.
arXiv Detail & Related papers (2023-10-24T15:20:07Z) - Classical stochastic representation of quantum mechanics [0.0]
We show that the dynamics of a quantum system can be represented by the dynamics of an underlying classical systems obeying the Hamilton equations of motion.
The probabilistic character of quantum mechanics is devised by treating the wave function as a variable.
arXiv Detail & Related papers (2023-07-31T21:02:43Z) - Continuously Monitored Quantum Systems beyond Lindblad Dynamics [68.8204255655161]
We study the probability distribution of the expectation value of a given observable over the possible quantum trajectories.
The measurements are applied to the entire system, having the effect of projecting the system into a product state.
arXiv Detail & Related papers (2023-05-06T18:09:17Z) - Non-commutative phase-space Lotka-Volterra dynamics: the quantum
analogue [0.0]
The Lotka-Volterra (LV) dynamics is investigated in the framework of the Weyl-Wigner (WW) quantum mechanics (QM)
The WW framework provides the ground for identifying how classical and quantum evolution coexist at different scales.
The generality of the framework developed here extends the boundaries of the understanding of quantum-like effects on competitive microscopical bio-systems.
arXiv Detail & Related papers (2022-06-14T11:23:04Z) - Quantum dynamics corresponding to chaotic BKL scenario [62.997667081978825]
Quantization smears the gravitational singularity avoiding its localization in the configuration space.
Results suggest that the generic singularity of general relativity can be avoided at quantum level.
arXiv Detail & Related papers (2022-04-24T13:32:45Z) - Efficient classical computation of expectation values in a class of
quantum circuits with an epistemically restricted phase space representation [0.0]
We devise a classical algorithm which efficiently computes the quantum expectation values arising in a class of continuous variable quantum circuits.
The classical computational algorithm exploits a specific restriction in classical phase space which directly captures the quantum uncertainty relation.
arXiv Detail & Related papers (2021-06-21T06:43:34Z) - Bernstein-Greene-Kruskal approach for the quantum Vlasov equation [91.3755431537592]
The one-dimensional stationary quantum Vlasov equation is analyzed using the energy as one of the dynamical variables.
In the semiclassical case where quantum tunneling effects are small, an infinite series solution is developed.
arXiv Detail & Related papers (2021-02-18T20:55:04Z) - Detecting dynamical quantum phase transition via out-of-time-order
correlations in a solid-state quantum simulator [12.059058714600607]
We develop and experimentally demonstrate that out-of-time-order correlators can be used to detect nonoequilibrium phase transitions in the transverse field Ising model.
Further applications of this protocol could enable studies other of exotic phenomena such as many body localization, and tests of the holographic duality between quantum and gravitational systems.
arXiv Detail & Related papers (2020-01-17T14:28:42Z)
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.