Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1103.4150 · Physical Review A

Finite-time quantum-to-classical transition for a Schrödinger-cat state

Janika Paavola, Michael J. W. Hall, Matteo G. A. Paris, Sabrina Maniscalco

Published Jul 27, 2011• 22 citations
arXivHTMLPDF

Abstract

The transition from quantum to classical, in the case of a quantum harmonic oscillator, is typically identified with the transition from a quantum superposition of macroscopically distinguishable states, such as the Schr\"odinger-cat state, into the corresponding statistical mixture. This transition is commonly characterized by the asymptotic loss of the interference term in the Wigner representation of the cat state. In this paper we show that the quantum-to-classical transition has different dynamical features depending on the measure for nonclassicality used. Measures based on an operatorial definition have well-defined physical meaning and allow a deeper understanding of the quantum-to-classical transition. Our analysis shows that, for most nonclassicality measures, the Schr\"odinger-cat state becomes classical after a finite time. Moreover, our results challenge the prevailing idea that more macroscopic states are more susceptible to decoherence in the sense that the transition from quantum to classical occurs faster. Since nonclassicality is a prerequisite for entanglement generation our results also bridge the gap between decoherence, which is lost only asymptotically, and entanglement, which may show a ``sudden death.'' In fact, whereas the loss of coherences still remains asymptotic, we emphasize that the transition from quantum to classical can indeed occur at a finite time.

DOI
10.1103/physreva.84.012121

Related papers

Quantum to classical transition induced by gravitational time dilation

Boris Sokolov, Iiro Vilja, Sabrina Maniscalco

We study the loss of quantumness caused by time dilation [I. Pikovski, M. Zych, F. Costa, and \ifmmode \check{C}\else \v{C}\fi{}. Brukner, Nat. Phys. 11, 668 (2015)] for a Schr\"odinger cat state. We give a holistic view of the quantum to classical transition by comparing the dynamics of several nonclassicality indicators, such as the Wigner function interference fringe, the negativity of the Wigner function, the nonclassical depth, the Vogel criterion, and the Klyshko criterion. Our results show that only two of these indicators depend critically on the size of the cat, namely, on how macroscopic the superposition is. Finally we compare the gravitation-induced decoherence times to the typical decoherence times due to classical noise originating from the unavoidable statistical fluctuations in the characteristic parameters of the system [J. Trapani, M. Bina, S. Maniscalco, and M. G. A. Paris, Phys. Rev. A 91, 022113 (2015)]. We show that the experimental observation of decoherence due to time dilation imposes severe limitations on the allowed levels of classical noise in the experiments.

arXiv:1702.02433•Physical Review A•Jul 26, 2017•9 citations

Non-Markovian Dynamics and the Quantum-To-Classical Transition for Quantum Brownian Motion

Janika Paavola

In this Thesis I discuss the dynamics of the quantum Brownian motion model in harmonic potential. This paradigmatic model has an exact solution, making it possible to consider also analytically the non-Markovian dynamics. The issues covered in this Thesis are themed around decoherence. First, I consider decoherence as the mediator of quantum-to-classical transition. I examine five different definitions for nonclassicality of quantum states, and show how each definition gives qualitatively different times for the onset of classicality. In particular I have found that all characterizations of nonclassicality, apart from one based on the interference term in the Wigner function, result in a finite, rather than asymptotic, time for the emergence of classicality. Second, I examine the diverse effects which coupling to a non-Markovian, structured reservoir, has on our system. By comparing different types of Ohmic reservoirs, I derive some general conclusions on the role of the reservoir spectrum in both the short-time and the thermalization dynamics. Finally, I apply these results to two schemes for decoherence control. Both of the methods are based on the non-Markovian properties of the dynamics.

•May 19, 2012•0 citations

Towards Schrödinger Cat States in the Second Harmonic Generation

Ranjit Singh, Leonid A. Barinov, Grigori G. Amosov +1 more

We investigate the quantum evolution of the pump field in second-harmonic generation under strong pump depletion. Starting from a coherent state, the pump develops a nonclassical phase-space structure resembling a Schrödinger cat state. This behavior originates from phase instability induced by vacuum fluctuations of the harmonic mode. A rigorous quantum analysis has been performed for mean photon numbers up to $\langle \hat n \rangle = 100$ in pump mode. For larger photon numbers, up to $\langle \hat n \rangle = 10^{7}$, the dynamics have been analyzed using a classical trajectory method with sampled initial conditions that reproduces the main features of the quantum evolution. The results indicate that nonlinear frequency conversion can generate macroscopic superposition-like states of the pump field. Although the resulting state is not pure due to correlations with the second-harmonic wave, it remains non-classical with negative zones of Wigner function. These results indicate that strongly nonlinear frequency conversion can provide a scalable route toward macroscopic nonclassical states of light.

quant-pharXiv:2603.24067•Mar 26, 2026•0 citations

Robust Negativity in the Quantum-to-Classical Transition of Kerr Dynamics

Mohsin Raza, John B. DeBrota, Ariel Shlosberg +2 more

We quantify the quantum-to-classical transition of the single-mode Kerr nonlinear dynamics in the presence of loss. We establish three time scales that govern the dynamics, each with distinct characteristics. For times short compared to the Ehrenfest time, the evolution is classical, characterized by Gaussian dynamics. For sufficiently long times, as we increase the initial photon number, unitary Kerr evolution would generate macroscopic superpositions of coherent states (so-called kitten states), but this is severely restricted in the presence of small photon loss so that expectation values of observables coincide with their classical values. The intermediate time scale, however, shows resilient quantum behavior in the macroscopic limit. We show that in the mean-field non-Gaussian regime, the Kerr Hamiltonian (with small photon loss) generates a significant amount of Wigner-negativity, and classical flow is recovered only if the loss rate grows with system size. Our results broaden the usual understanding of quantum-to-classical transitions and demonstrate the potential for creating robust nonclassical resources for continuous-variable quantum information processing in the presence of loss.

quant-pharXiv:2602.05223•Physical Review A•Feb 6, 2026•0 citations

Collapse and revival of quantum coherence for a harmonic oscillator interacting with a classical fluctuating environment

Jacopo Trapani, Matteo Bina, Sabrina Maniscalco +1 more

We address the dynamics of nonclassicality for a quantum system interacting with a noisy fluctuating environment described by a classical stochastic field. As a paradigmatic example, we consider a harmonic oscillator initially prepared in a maximally nonclassical state, e.g., a Fock number state or a Schr\"odinger-cat-like state, and then coupled to either a resonant or a nonresonant external field. Stochastic modeling allows us to describe the decoherence dynamics without resorting to approximated quantum master equations and to introduce non-Markovian effects in a controlled way. A detailed comparison among different nonclassicality criteria and a thorough analysis of the decoherence time reveal a rich phenomenology whose main features may be summarized as follows: (i) Classical memory effects increase the survival time of quantum coherence and (ii) a detuning between the natural frequency of the system and the central frequency of the classical field induces revivals of quantum coherence.

arXiv:1411.0946•Physical Review A•Feb 17, 2015•35 citations

Quantum Zeno control of decoherence

Sabrina Maniscalco

We demonstrate the possibility of controlling the quantum to classical transition by means of the quantum Zeno and anti-Zeno effects. We consider a quantum harmonic oscillator initially prepared in a Schrödinger cat state and interacting with an engineered amplitude reservoir. We show that the environment induced decoherence transforming the cat state into a statistical mixture can be strongly inhibited by means of either appropriate sequences of measurements or shuttered reservoirs.

Laser Physics•Apr 2, 2010•2 citations
The transition from quantum to classical, in the case of a quantum harmonic oscillator, is typically identified with the transition from a quantum superposition of macroscopically distinguishable states, such as the Schr"odinger-cat state, into the corresponding statistical mixture. This transition is commonly characterized by the asymptotic loss of the interference term in the Wigner representation of the cat state. In this paper we show that the quantum-to-classical transition has different dynamical features depending on the measure for nonclassicality used. Measures based on an operatorial definition have well-defined physical meaning and allow a deeper understanding of the quantum-to-classical transition. Our analysis shows that, for most nonclassicality measures, the Schr"odinger-cat state becomes classical after a finite time. Moreover, our results challenge the prevailing idea that more macroscopic states are more susceptible to decoherence in the sense that the transition from quantum to classical occurs faster. Since nonclassicality is a prerequisite for entanglement generation our results also bridge the gap between decoherence, which is lost only asymptotically, and entanglement, which may show a ``sudden death.'' In fact, whereas the loss of coherences still remains asymptotic, we emphasize that the transition from quantum to classical can indeed occur at a finite time.
We study the loss of quantumness caused by time dilation [I. Pikovski, M. Zych, F. Costa, and \ifmmode \check{C}\else \v{C}\fi{}. Brukner, Nat. Phys. 11, 668 (2015)] for a Schr\"odinger cat state. We give a holistic view of the quantum to classical transition by comparing the dynamics of several nonclassicality indicators, such as the Wigner function interference fringe, the negativity of the Wigner function, the nonclassical depth, the Vogel criterion, and the Klyshko criterion. Our results show that only two of these indicators depend critically on the size of the cat, namely, on how macroscopic the superposition is. Finally we compare the gravitation-induced decoherence times to the typical decoherence times due to classical noise originating from the unavoidable statistical fluctuations in the characteristic parameters of the system [J. Trapani, M. Bina, S. Maniscalco, and M. G. A. Paris, Phys. Rev. A 91, 022113 (2015)]. We show that the experimental observation of decoherence due to time dilation imposes severe limitations on the allowed levels of classical noise in the experiments.
In this Thesis I discuss the dynamics of the quantum Brownian motion model in harmonic potential. This paradigmatic model has an exact solution, making it possible to consider also analytically the non-Markovian dynamics. The issues covered in this Thesis are themed around decoherence. First, I consider decoherence as the mediator of quantum-to-classical transition. I examine five different definitions for nonclassicality of quantum states, and show how each definition gives qualitatively different times for the onset of classicality. In particular I have found that all characterizations of nonclassicality, apart from one based on the interference term in the Wigner function, result in a finite, rather than asymptotic, time for the emergence of classicality. Second, I examine the diverse effects which coupling to a non-Markovian, structured reservoir, has on our system. By comparing different types of Ohmic reservoirs, I derive some general conclusions on the role of the reservoir spectrum in both the short-time and the thermalization dynamics. Finally, I apply these results to two schemes for decoherence control. Both of the methods are based on the non-Markovian properties of the dynamics.
We investigate the quantum evolution of the pump field in second-harmonic generation under strong pump depletion. Starting from a coherent state, the pump develops a nonclassical phase-space structure resembling a Schrödinger cat state. This behavior originates from phase instability induced by vacuum fluctuations of the harmonic mode. A rigorous quantum analysis has been performed for mean photon numbers up to ⟨n^⟩=100\langle \hat n \rangle = 100⟨n^⟩=100 in pump mode. For larger photon numbers, up to ⟨n^⟩=107\langle \hat n \rangle = 10^{7}⟨n^⟩=107, the dynamics have been analyzed using a classical trajectory method with sampled initial conditions that reproduces the main features of the quantum evolution. The results indicate that nonlinear frequency conversion can generate macroscopic superposition-like states of the pump field. Although the resulting state is not pure due to correlations with the second-harmonic wave, it remains non-classical with negative zones of Wigner function. These results indicate that strongly nonlinear frequency conversion can provide a scalable route toward macroscopic nonclassical states of light.
We quantify the quantum-to-classical transition of the single-mode Kerr nonlinear dynamics in the presence of loss. We establish three time scales that govern the dynamics, each with distinct characteristics. For times short compared to the Ehrenfest time, the evolution is classical, characterized by Gaussian dynamics. For sufficiently long times, as we increase the initial photon number, unitary Kerr evolution would generate macroscopic superpositions of coherent states (so-called kitten states), but this is severely restricted in the presence of small photon loss so that expectation values of observables coincide with their classical values. The intermediate time scale, however, shows resilient quantum behavior in the macroscopic limit. We show that in the mean-field non-Gaussian regime, the Kerr Hamiltonian (with small photon loss) generates a significant amount of Wigner-negativity, and classical flow is recovered only if the loss rate grows with system size. Our results broaden the usual understanding of quantum-to-classical transitions and demonstrate the potential for creating robust nonclassical resources for continuous-variable quantum information processing in the presence of loss.
We address the dynamics of nonclassicality for a quantum system interacting with a noisy fluctuating environment described by a classical stochastic field. As a paradigmatic example, we consider a harmonic oscillator initially prepared in a maximally nonclassical state, e.g., a Fock number state or a Schr\"odinger-cat-like state, and then coupled to either a resonant or a nonresonant external field. Stochastic modeling allows us to describe the decoherence dynamics without resorting to approximated quantum master equations and to introduce non-Markovian effects in a controlled way. A detailed comparison among different nonclassicality criteria and a thorough analysis of the decoherence time reveal a rich phenomenology whose main features may be summarized as follows: (i) Classical memory effects increase the survival time of quantum coherence and (ii) a detuning between the natural frequency of the system and the central frequency of the classical field induces revivals of quantum coherence.