Coherent-State Kernels for Composite Quantum Operations
Abstract
This paper develops a unified kernel-based method for computing exact matrix elements of composite quantum operations by inserting resolutions of the identity after individual operators or between successive factors of an operator chain. A single insertion gives an exact scalar identity, and nested insertions between the factors give multiple integral identities for chains of closed operators under explicit Bochner-integrability conditions. The procedure is carried through on polynomial and analytic functions of the ladder operators, on one- and two-mode Gaussian unitaries, and on three composite operations: a Kerr phase followed by squeezing or by a cubic phase gate, a two-mode squeezer followed by a beam splitter, and a heralded cat-state circuit with two beam splitters. At rational Kerr phases the Kerr-squeezed amplitudes reduce to finite sums of squeezed coherent-state amplitudes weighted by quadratic Gauss sums, with an explicit error bound at the remaining phases; the two-mode network gives a bivariate Hermite polynomial; and the heralded circuit gives closed forms for the amplitudes, the heralding probabilities and their extension to an arbitrary passive network fed by one squeezed source. The examples are set against the reach of four established techniques: operator ordering, the Berezin symbol calculus, Lie disentangling and the symplectic formalism. Each technique reaches a subset of the examples directly, while the insertion procedure reaches all of them under the same hypotheses. A comparison with direct Fock summation identifies the regime in which the finite Kerr sums are efficient, and the choice of resolution at each boundary of a chain follows a selection rule set by the action of the adjacent factor. Each closed form agrees with an independent numerical computation.
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BibTeX
@misc{cordshooli2026coherentstate,
title = {{Coherent-State Kernels for Composite Quantum Operations}},
author = {Ghasem Asadi Cordshooli},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.23240},
eprint = {2607.23240},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.23240},
}
RIS
TY - UNPB
TI - Coherent-State Kernels for Composite Quantum Operations
AU - Ghasem Asadi Cordshooli
PY - 2026
DA - 2026/10/15
PB - arXiv
DO - 10.48550/arxiv.2607.23240
UR - https://arxiv.org/abs/2607.23240
AB - This paper develops a unified kernel-based method for computing exact matrix elements of composite quantum operations by inserting resolutions of the identity after individual operators or between successive factors of an operator chain. A single insertion gives an exact scalar identity, and nested insertions between the factors give multiple integral identities for chains of closed operators under explicit Bochner-integrability conditions. The procedure is carried through on polynomial and analytic functions of the ladder operators, on one- and two-mode Gaussian unitaries, and on three composite operations: a Kerr phase followed by squeezing or by a cubic phase gate, a two-mode squeezer followed by a beam splitter, and a heralded cat-state circuit with two beam splitters. At rational Kerr phases the Kerr-squeezed amplitudes reduce to finite sums of squeezed coherent-state amplitudes weighted by quadratic Gauss sums, with an explicit error bound at the remaining phases; the two-mode network gives a bivariate Hermite polynomial; and the heralded circuit gives closed forms for the amplitudes, the heralding probabilities and their extension to an arbitrary passive network fed by one squeezed source. The examples are set against the reach of four established techniques: operator ordering, the Berezin symbol calculus, Lie disentangling and the symplectic formalism. Each technique reaches a subset of the examples directly, while the insertion procedure reaches all of them under the same hypotheses. A comparison with direct Fock summation identifies the regime in which the finite Kerr sums are efficient, and the choice of resolution at each boundary of a chain follows a selection rule set by the action of the adjacent factor. Each closed form agrees with an independent numerical computation.
ER -