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

• Published in: arXiv.org
• Main Authors: Shukla, Atharva, Sanders, Barry C
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 24.10.2023
• Subjects: Directional sensitivity; Physics - Quantum Physics
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.2306.13182

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.