Sub-Planck structure in a mixed state

Abstract

The persistence of sub-Planck structure in phase space with loss of coherence is demonstrated in a mixed state, which comprises two terms in the density matrix. Its utility in carrying out Heisenberg-limited measurement and quantum parameter estimation have been shown. It is also shown that the mixed state performs equally well as the compass state for carrying out precision measurements. The advantage of using mixed state relies on the fact that such a state can be easier to prepare and may appear from pure states after partial loss of coherence. We explicate the effect of environment on these sub-Planck structures in the mixed state and estimates the time scale of complete decoherence.

References in corpus (17)

• Decoherence, einselection, and the quantum origins of the classical
• Observation of quantum state collapse and revival due to the single-photon Kerr effect
• Sub-Planck spots of Schroedinger cats and quantum decoherence
• Alternative Derivation of the Hu-Paz-Zhang Master Equation for Quantum Brownian Motion
• Exact solution of the Hu-Paz-Zhang master equation
• Sub-Planck phase-space structures and Heisenberg-limited measurements
• Introduction to decoherence theory
• Mesoscopic Superposition of States with Sub-Planck Structures in Phase Space
• Sub-Planck scale structures in the P{ö}schl-Teller potential and their sensitivity to perturbations
• Mesoscopic superposition and sub-Planck-scale structure in molecular wave packets
• Time-frequency Domain Analogues of Phase Space Sub-Planck Structures
• Sub-Planck scale structures in a vibrating molecule in the presence of decoherence
• Entanglement induced Sub-Planck structures
• Phase Space Structure of Generalized Gaussian Cat States
• Limitations on the Utility of Exact Master Equations
• Transition to sub-Planck structures through the superposition of q-oscillator stationary states
• Cat state, sub-Planck structure and weak measurement

Cited by in corpus (6)

• Sub-Planck phase-space structure and sensitivity for SU(1,1) compass states
• Sub-Planck structures: Analogies between the Heisenberg-Weyl and SU(2) groups
• Sensing Single Photon in a Cat State
• Sub-Planck structures and sensitivity of the superposed photon-added or photon-subtracted squeezed-vacuum states
• Superposing compass states for asymptotic isotropic sub-Planck phase-space sensitivity
• Generalized Entanglement Measure for Continuous Variable Systems