Superposing compass states for asymptotic isotropic sub-Planck phase-space sensitivity

Abstract

Compass states deliver sub-Planck phase-space structure in the sense that sensitivity to phase-space displacement is superior to the sensitivity of displacing the vacuum state in any direction, but this sensitivity is anisotropic: better sensitivity for some directions of phase-space displacement vs others. Here we introduce generalised compass states as superpositions of $n$ compass states, with each oriented by $\frac{\pi }{2n}$ with respect to its predecessor. Specifically, we derive Wigner functions for these generalised compass states and approximate closed-form expressions for overlaps between generalised compass states and their displaced counterparts. Furthermore, we show that generalised compass states, in the limit $n\to \infty$, display isotropic sensitivity to phase-space displacement in any direction.

arXiv comment15 pages, 6 figures

References in corpus (22)

• Sub-Planck spots of Schroedinger cats and quantum decoherence
• Breeding the optical Schroedinger's cat state
• Sub-Planck phase-space structures and Heisenberg-limited measurements
• Decay of the Loschmidt Echo for quantum states with sub-Planck scale structures
• Wigner Function Evolution of Quantum States in Presence of Self-Kerr Interaction
• Mesoscopic Superposition of States with Sub-Planck Structures in Phase Space
• Experimental Observation of Quantum Chaos in a Beam of Light
• Quantum metrology at the Heisenberg limit with ion traps
• Short time decay of the Loschmidt echo
• Generation of a superposition of multiple mesoscopic states of radiation in a resonant cavity
• Sub-Planck scale structures in the P{ö}schl-Teller potential and their sensitivity to perturbations
• Time-frequency Domain Analogues of Phase Space Sub-Planck Structures
• Mesoscopic superposition and sub-Planck-scale structure in molecular wave packets
• Sub-Planck scale structures in a vibrating molecule in the presence of decoherence
• Entanglement induced Sub-Planck structures
• Quantum Hypercube States
• 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
• Teleportation fidelity as a probe of sub-Planck phase-space structure
• Direct Measurement of Time-Frequency Analogues of Sub-Planck Structures
• Measuring sub-Planck structural analogues in chronocyclic phase space
• Sub-Planck structure in a mixed state

Cited by in corpus (7)

• Quantum metrology with a continuous-variable system
• Compasslike states in a thermal reservoir and fragility of their nonclassical features
• Multicomponent cat states with sub-Planckian structures and their optomechanical analogues
• Optimal Phase-Insensitive Force Sensing with Non-Gaussian States
• Sub-shot-noise sensitivity via superpositions of two deformed kitten states
• Nonclassicality and sub-Planck structures of photon subtracted compass states
• Covariant operator bases for continuous variables