Mesoscopic quantum superposition of the generalized cat state: A diffraction limit

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.

Two Mode Photon Added Schrödinger Cat States: Nonclassicality and Entanglement

“…In a quantum optics research, two-mode cat state is generally used as an entangled tool, which cannot be distilled only by classical communications due to the limitation from the no-go theorem [20]. To suffice the condition of quantum information protocols for long-distance communication, there have been suggestions and realizations for manipulating the quantum states, which are reasonable ways to conditionally operate a nonclassical state [21][22][23] of an optical field by subtracting or adding photons from/to a optical states [2,13,15,24]. Actually, the photon addition and subtraction have been successfully demonstrated experimentally for probing quantum commutation rules by Parigi et al [25].…”

The Simultaneity Requirement of Quantum Superposition Principle

“…The superposition principle is one of the basic foundations of quantum mechanics [1]. Quantum superposition is responsible for various new phenomena [2][3]. The understanding of quantum superposition principle is very important.…”

Method to deterministically generate large-amplitude optical cat states

“…With the increase of amplitude |α|, CS gets closer to the macroscopic superposition, making it an important resource for the study of macroscopic quantum phenomena. CS is not only attractive from a fundamental point of view 2,3 , but also valuable for applications including quantum teleportation [4][5][6] , quantum computing [7][8][9][10][11] , quantum error correction [12][13][14][15][16][17] and quantum metrology [18][19][20][21][22][23][24] . After decades of efforts, CS is now being generated on various platforms 3,[25][26][27][28] .…”