Predictability sieve, pointer states, and the classicality of quantum trajectories

Abstract

We study various measures of classicality of the states of open quantum systems subject to decoherence. Classical states are expected to be stable in spite of decoherence, and are thought to leave conspicuous imprints on the environment. Here these expected features of environment-induced superselection (einselection) are quantified using four different criteria: predictability sieve (which selects states that produce least entropy), purification time (which looks for states that are the easiest to find out from the imprint they leave on the environment), efficiency threshold (which finds states that can be deduced from measurements on a smallest fraction of the environment), and purity loss time (that looks for states for which it takes the longest to lose a set fraction of their initial purity). We show that when pointer states -- the most predictable states of an open quantum system selected by the predictability sieve -- are well defined, all four criteria agree that they are indeed the most classical states. We illustrate this with two examples: an underdamped harmonic oscillator, for which coherent states are unanimously chosen by all criteria, and a free particle undergoing quantum Brownian motion, for which most criteria select almost identical Gaussian states (although, in this case, predictability sieve does not select well defined pointer states.)

10 pages, 13 figures

References in corpus (20)

• Decoherence, einselection, and the quantum origins of the classical
• Continuous quantum measurement and Itô formalism
• Measurements continuous in time and a posteriori states in quantum
• Einselection and Decoherence from an Information Theory Perspective
• Objective properties from subjective quantum states: Environment as a witness
• Continuous Quantum Measurement and the Emergence of Classical Chaos
• Complete parameterization, and invariance, of diffusive quantum trajectories for Markovian open systems
• Quantum state diffusion, localization and computation
• Decoherence of Quantum Fields: Pointer States and Predictability
• The Emergence of Classicality via Decoherence Described by Lindblad Operators
• Decoherence produces coherent states: an explicit proof for harmonic chains
• Non-Markovian quantum feedback from homodyne measurements: the effect of a non-zero feedback delay time
• Cat States and Single Runs for the Damped Harmonic Oscillator
• Unconditional Pointer States from Conditional Master Equations
• Improvement of measurement accuracy in SU(1,1) interferometers
• Maximally Robust Unravelings of Quantum Master Equations
• Conditional quantum dynamics with several observers
• Robust unravelings for resonance fluorescence
• Atom Lasers, Coherent States, and Coherence:II. Maximally Robust Ensembles of Pure States
• Classical Robustness of Quantum Unravellings

Cited by in corpus (22)

• Quantum Darwinism: Entanglement, branches, and the emergent classicality of redundantly stored quantum information
• Consciousness as a State of Matter
• Variational Consistent Histories as a Hybrid Algorithm for Quantum Foundations
• The Objective Past of a Quantum Universe: Redundant Records of Consistent Histories
• Quantum Theory of the Classical: Einselection, Envariance, Quantum Darwinism and Extantons
• Generalized Coherent States as Preferred States of Open Quantum Systems
• Intrinsic Quantum Computation
• Coherent states for generalized uncertainty relations as Tsallis probability amplitudes: new route to non-extensive thermostatistics
• Unraveling Quantum Brownian Motion: Pointer States and their Classical Trajectories
• Diffraction limit of the sub-Planck structures
• Dynamics of Open Bosonic Quantum Systems in Coherent State Representation
• Decoherence and pointer states in small antiferromagnets: A benchmark test
• Decoherence, Time Scales and Pointer States
• Adapted Caldeira-Leggett Model
• Quantum Uncertainties in the Schmidt Basis Given by Decoherence
• Semiclassical Coulomb field
• Quantum Brownian motion as an iterated entanglement-breaking measurement by the environment
• A Generalized Master Equation for Janus Faced Coherent States
• Classical limit of entangled states of two angular momenta
• An open scattering model in polymerized quantum mechanics
• Does Decoherence Make Observations Classical?
• Decoherence limit of quantum systems obeying generalized uncertainty principle: new paradigm for Tsallis thermostatistics