We present evidence that decoherence can produce a smooth quantum-to-classical transition in nonlinear dynamical systems. High-resolution tracking of quantum and classical evolutions reveals differences in expectation values of corresponding observables. Solutions of master equations demonstrate that decoherence destroys quantum interference in Wigner distributions and washes out fine structure in classical distributions, bringing the two closer together. Correspondence between quantum and classical expectation values is also reestablished.We present evidence that decoherence can produce a smooth quantum-to-classical transition in nonlinear dynamical systems. High-resolution tracking of quantum and classical evolutions reveals differences in expectation values of corresponding observables. Solutions of master equations demonstrate that decoherence destroys quantum interference in Wigner distributions and washes out fine structure in classical distributions, bringing the two closer together. Correspondence between quantum and classical expectation values is also reestablished.

arXiv:quant-ph/9803042Physical Review LettersMay 18, 1998252 citations

Decoherence effects in the Wigner function formalism

Philipp Schwaha, Damien Querlioz, Philippe Dollfus +3 more

Journal of Computational ElectronicsJun 11, 201312 citations

Inequivalent ways to apply semiclassical smoothing to a quantum system

Kiarn T. Laverick, Areeya Chantasri, Howard M. Wiseman

In this paper, we correct a mistake we made in [Phys. Rev. Lett. $\textbf{122}$ , 190402 (2019)] and [Phys. Rev. A $\textbf{103}$ , 012213 (2021)] regarding the Wigner function of the so-called smoothed Weak-Valued state (SWV state). Here smoothing refers to estimation of properties at time $t$ using information obtained in measurements both before and after $t$ . The SWV state is a pseudo-state (Hermitian but not necessarily positive) that gives, by the usual trace formula, the correct value for a weak measurement preformed at time $t$ , $\textit{i.e.}$ , its weak value. The Wigner function is a pseudo-probability-distribution (real but not necessarily positive) over phase-space. A smoothed (in this estimation sense) Wigner distribution at time $t$ can also be defined by applying classical smoothing for probability-distributions to the Wigner functions. The smoothed Wigner distribution (SWD) gives identical means for the canonical phase-space variables as does the SWV state. However, contrary to the assumption in the above references, the Wigner function of the SWV state is not the smoothed Wigner distribution.In this paper, we correct a mistake we made in [Phys. Rev. Lett. $\textbf{122}$, 190402 (2019)] and [Phys. Rev. A $\textbf{103}$, 012213 (2021)] regarding the Wigner function of the so-called smoothed Weak-Valued state (SWV state). Here smoothing refers to estimation of properties at time $t$ using information obtained in measurements both before and after $t$. The SWV state is a pseudo-state (Hermitian but not necessarily positive) that gives, by the usual trace formula, the correct value for a weak measurement preformed at time $t$, $\textit{i.e.}$, its weak value. The Wigner function is a pseudo-probability-distribution (real but not necessarily positive) over phase-space. A smoothed (in this estimation sense) Wigner distribution at time $t$ can also be defined by applying classical smoothing for probability-distributions to the Wigner functions. The smoothed Wigner distribution (SWD) gives identical means for the canonical phase-space variables as does the SWV state. However, contrary to the assumption in the above references, the Wigner function of the SWV state is not the smoothed Wigner distribution.

arXiv:2505.00341Physical Review AJul 21, 20252 citations

Wigner quasi-probability distribution of a resonator coherent field interacting with a flux qubit via two-photon coupling

Laila A. Al‐Essa, Wafa F. Alfwzan, F. M. Aldosari +2 more

The Wigner quasi-probability distribution function is an important tool for estimating the quantumness of quantum states. The Wigner distribution function (WDF) is related monotonically to the coherent field state density operator and their probability distributions. In this paper, we analyze the time-dependent resonator coherent field states produced by a flux qubit’s interaction with a resonator through a two-photon coupling. The WDF dynamics of the coherent field states is investigated under the effects of the qubit-resonator detuning and the intrinsic decoherence. The WDF non-classicality associated with the mixedness resonator entropy dynamics can be controlled by varying the qubit-resonator interaction, detuning as well as the decoherence. The intrinsic decoherence clearly affects the WDF non-classicality, identified by the negative values of the WDF. Finally, by fixing one or both of the complex phase space components, we are able to explore the dynamics of the Wigner-distribution functions.The Wigner quasi-probability distribution function is an important tool for estimating the quantumness of quantum states. The Wigner distribution function (WDF) is related monotonically to the coherent field state density operator and their probability distributions. In this paper, we analyze the time-dependent resonator coherent field states produced by a flux qubit’s interaction with a resonator through a two-photon coupling. The WDF dynamics of the coherent field states is investigated under the effects of the qubit-resonator detuning and the intrinsic decoherence. The WDF non-classicality associated with the mixedness resonator entropy dynamics can be controlled by varying the qubit-resonator interaction, detuning as well as the decoherence. The intrinsic decoherence clearly affects the WDF non-classicality, identified by the negative values of the WDF. Finally, by fixing one or both of the complex phase space components, we are able to explore the dynamics of the Wigner-distribution functions.

Results in PhysicsNov 3, 20230 citations

In this paper, we correct a mistake we made in [Phys. Rev. Lett.

\textbf{122}

, 190402 (2019)] and [Phys. Rev. A

\textbf{103}

, 012213 (2021)] regarding the Wigner function of the so-called smoothed Weak-Valued state (SWV state). Here smoothing refers to estimation of properties at time

t

using information obtained in measurements both before and after

t

. The SWV state is a pseudo-state (Hermitian but not necessarily positive) that gives, by the usual trace formula, the correct value for a weak measurement preformed at time

t

\textit{i.e.}

, its weak value. The Wigner function is a pseudo-probability-distribution (real but not necessarily positive) over phase-space. A smoothed (in this estimation sense) Wigner distribution at time

t

can also be defined by applying classical smoothing for probability-distributions to the Wigner functions. The smoothed Wigner distribution (SWD) gives identical means for the canonical phase-space variables as does the SWV state. However, contrary to the assumption in the above references, the Wigner function of the SWV state is not the smoothed Wigner distribution.