Diffraction limit of the sub-Planck structures

Abstract

The orthogonality of cat and displaced cat states, underlying Heisenberg limited measurement in quantum metrology, is studied in the limit of large number of states. The asymptotic expression for the corresponding state overlap function, controlled by the sub-Planck structures arising from phase space interference, is obtained exactly. The validity of large phase space support, in which context the asymptotic limit is achieved, is discussed in detail. For large number of coherent states, uniformly located on a circle, it identically matches with the diffraction pattern for a circular ring with uniform angular source strength. This is in accordance with the van Cittert-Zernike theorem, where the overlap function, similar to the mutual coherence function matches with a diffraction pattern.

5 pages, 3 figures

References in corpus (6)

• Quantum Darwinism
• Sub-Planck scale structures in the P{ö}schl-Teller potential and their sensitivity to perturbations
• Sub-Planck scale structures in a vibrating molecule in the presence of decoherence
• Entanglement induced Sub-Planck structures
• Coherent control of mesoscopic superpositions in a diatomic molecule
• Enhanced Quantum Sensitivity in a Vibrating Diatomic Molecule due to Rotational Amendment

Cited by in corpus (2)

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