Quantum Sensitivity of N-Component Cat States
Abstract
We extend our previous study of squeezed two-component Schrödinger cat states to a phase-referenced single-mode family with an arbitrary number N of coherent components and general relative phases. Within the established circular-state construction, we derive a closed complex overlap kernel for the ordered action of displacement, phase rotation, and squeezing, retaining exact finite-amplitude normalization. We distinguish finite-displacement orthogonality from local phase-estimation sensitivity quantified by quantum Fisher information (QFI). For equal-phase states, we compare N=2,…,9 at a common mean photon number and include coherent-state and squeezed-vacuum benchmarks. A bound on the higher photon-number sectors establishes the fixed-energy asymptote FQ,N=4n̅(N−n̅)+o(1). Its leading term agrees with the known QFI of a vacuum--N-photon superposition. The resulting decrease of the ideal local quantum Cramér--Rao bound does not establish unlimited attainable precision: prior phase information, sample size, phase-reference resources, optical loss, state preparation, and measurement choice remain relevant.
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BibTeX
@misc{singh2026quantum,
title = {{Quantum Sensitivity of $N$-Component Cat States}},
author = {Ranjit Singh and Alexander E. Teretenkov},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.23398},
eprint = {2610.23398},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.23398},
}
RIS
TY - UNPB
TI - Quantum Sensitivity of N-Component Cat States
AU - Ranjit Singh
AU - Alexander E. Teretenkov
PY - 2026
DA - 2026/10/16
PB - arXiv
DO - 10.48550/arxiv.2610.23398
UR - https://arxiv.org/abs/2610.23398
AB - We extend our previous study of squeezed two-component Schrödinger cat states to a phase-referenced single-mode family with an arbitrary number N of coherent components and general relative phases. Within the established circular-state construction, we derive a closed complex overlap kernel for the ordered action of displacement, phase rotation, and squeezing, retaining exact finite-amplitude normalization. We distinguish finite-displacement orthogonality from local phase-estimation sensitivity quantified by quantum Fisher information (QFI). For equal-phase states, we compare N=2,…,9 at a common mean photon number and include coherent-state and squeezed-vacuum benchmarks. A bound on the higher photon-number sectors establishes the fixed-energy asymptote F_Q,N=4n̅(N−n̅)+o(1). Its leading term agrees with the known QFI of a vacuum--N-photon superposition. The resulting decrease of the ideal local quantum Cramér--Rao bound does not establish unlimited attainable precision: prior phase information, sample size, phase-reference resources, optical loss, state preparation, and measurement choice remain relevant.
ER -