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

Abstract

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.

v2: minor changes. v1: 14+15 pages, 12+3 figures, comments welcome

References in corpus (38)

• Quantum Computing in the NISQ era and beyond
• Decoherence, einselection, and the quantum origins of the classical
• Encoding a qubit in an oscillator
• Error mitigation for short-depth quantum circuits
• Phase space representation of quantum dynamics
• Decoherence, Chaos, and the Second Law
• Positive Wigner functions render classical simulation of quantum computation efficient
• Blueprint for a Scalable Photonic Fault-Tolerant Quantum Computer
• Decoherence, Chaos, and the Correspondence Principle
• Resource theory of quantum non-Gaussianity and Wigner negativity
• Estimating outcome probabilities of quantum circuits using quasiprobabilities
• Propagating Gottesman-Kitaev-Preskill states encoded in an optical oscillator
• Decoherence, chaos, quantum-classical correspondence, and the algorithmic arrow of time
• All-optical generation of states for "Encoding a qubit in an oscillator"
• Generation of discrete superpositions of coherent states in the anharmonic oscillator model
• Classical to Quantum Transition of a Driven Nonlinear Nanomechanical Resonator
• Non-Gaussian states for continuous variable quantum computation via Gaussian maps
• Wigner Function Evolution of Quantum States in Presence of Self-Kerr Interaction
• Engineering a Kerr-based Deterministic Cubic Phase Gate via Gaussian Operations
• Macroscopic Quantum Superpositions via Dynamics in a Wide Double-Well Potential
• Exact solutions of interacting dissipative systems via weak symmetries
• Fast Quantum Interference of a Nanoparticle via Optical Potential Control
• Decoherence of multi-dimensional entangled coherent states
• Gaussian conversion protocols for cubic phase state generation
• Third quantization of open quantum systems: new dissipative symmetries and connections to phase-space and Keldysh field theory formulations
• Gaussian Quantum Trajectories for the Variational Simulation of Open Quantum-Optical Systems
• Generation of Flying Logical Qubits using Generalized Photon Subtraction with Adaptive Gaussian Operations
• Cubic nonlinear squeezing and its decoherence
• Generation of quantum states with nonlinear squeezing by Kerr nonlinearity
• Quadrature squeezing enhances Wigner negativity in a mechanical Duffing oscillator
• Semiclassical Description of Wavepacket Revival
• Survival of quantum effects for observables after decoherence
• Wigner Analysis of Particle Dynamics and Decoherence in Wide Nonharmonic Potentials
• Effective generation of cat and kitten states
• Classical correspondence beyond the Ehrenfest time for open quantum systems with general Lindbladians
• Moyal phase-space analysis of nonlinear optical Kerr media
• Nonlinear Phase Gates as Airy Transforms of the Wigner Function
• Decoherence Limits the Cost to Simulate an Anharmonic Oscillator