Discrete quadrature spectrum of composite bosons: Weyl relation, intensity correlations, and binned homodyne detection
Abstract
A composite boson made of two fermions can look elementary under one measurement and composite under another. In an exactly solvable paired-mode model we compare three probes: classical drives, periodically binned quadrature statistics, and intensity correlations g(2). The Weyl defect has an exact product formula and a controlled dilute expansion in the Schmidt moments. The binned observables are instead piecewise constant in the Schmidt weights and sensitive to single eigenvalues crossing bin edges; on the flat-spectrum ladder they converge slowly and nonmonotonically over the computed range. A spectral filter and a polar correction recover an exact Pauli algebra; a heralded joint projection then extracts a logical singlet from the vacua of two independent copies of the composite, with probability set by the accepted weight and the mixedness of the filtered reduced qubit. Finite-mode examples with Schmidt number about three succeed at the percent level despite order-one Weyl defects; near-unit g(2) does not control the binned algebra. For flat spectra the construction converges strongly to its oscillator counterpart, whose vacuum overlap is strictly positive at every scale; for infinite spectra with summable Schmidt amplitudes it converges at all but countably many filter cutoffs, positivity at the cutoffs studied remaining open.
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BibTeX
@misc{roditi2026discrete,
title = {{Discrete quadrature spectrum of composite bosons: Weyl relation, intensity correlations, and binned homodyne detection}},
author = {Itzhak Roditi},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.07776},
eprint = {2611.07776},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.07776},
}
RIS
TY - UNPB
TI - Discrete quadrature spectrum of composite bosons: Weyl relation, intensity correlations, and binned homodyne detection
AU - Itzhak Roditi
PY - 2026
DA - 2026/11/05
PB - arXiv
DO - 10.48550/arxiv.2611.07776
UR - https://arxiv.org/abs/2611.07776
AB - A composite boson made of two fermions can look elementary under one measurement and composite under another. In an exactly solvable paired-mode model we compare three probes: classical drives, periodically binned quadrature statistics, and intensity correlations g^(2). The Weyl defect has an exact product formula and a controlled dilute expansion in the Schmidt moments. The binned observables are instead piecewise constant in the Schmidt weights and sensitive to single eigenvalues crossing bin edges; on the flat-spectrum ladder they converge slowly and nonmonotonically over the computed range. A spectral filter and a polar correction recover an exact Pauli algebra; a heralded joint projection then extracts a logical singlet from the vacua of two independent copies of the composite, with probability set by the accepted weight and the mixedness of the filtered reduced qubit. Finite-mode examples with Schmidt number about three succeed at the percent level despite order-one Weyl defects; near-unit g^(2) does not control the binned algebra. For flat spectra the construction converges strongly to its oscillator counterpart, whose vacuum overlap is strictly positive at every scale; for infinite spectra with summable Schmidt amplitudes it converges at all but countably many filter cutoffs, positivity at the cutoffs studied remaining open.
ER -