Negative quasiprobabilities redistribute (and complex ones reduce) the information in unabsorbed photons
Abstract
Negative Kirkwood--Dirac quasiprobabilities are credited with the quantum advantage of interaction-free measurement and postselected metrology. We test that claim on the task interaction-free measurement was designed for: learning about a sample letting it absorb as little light as possible. The Kirkwood--Dirac distribution of path and output gives the linear response to a weak sample: its real part responds to absorption, its imaginary part to a phase. For a pure single photon passing once through any interferometer, the Fisher information about transmittance per absorbed photon is the direct-transmission value minus a sum of squared imaginary parts: no interferometer or readout beats direct transmission. Negativity plays no role beyond concentrating information in weakly lit outputs. The imaginary parts of the Kirkwood-Dirac distribution depend on the output basis here, not on the sample, so a basis exists in which every term is real, which is optimal. A single photon gains information per absorbed photon only through a phase response, which for an optical line needs a thick or inhomogeneously broadened sample, or through many passes when absorptions go uncounted, as shown by a critically coupled resonator. For detecting a weak absorber, negativity gives a single-shot advantage that does not accumulate over multiple trials; advantage instead accumulates when there are outputs which are dark without the object, a case which needs no negativity.
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BibTeX
@misc{hance2026negative,
title = {{Negative quasiprobabilities redistribute (and complex ones reduce) the information in unabsorbed photons}},
author = {Jonte R. Hance},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.00740},
eprint = {2610.00740},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.00740},
}
RIS
TY - UNPB
TI - Negative quasiprobabilities redistribute (and complex ones reduce) the information in unabsorbed photons
AU - Jonte R. Hance
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.00740
UR - https://arxiv.org/abs/2610.00740
AB - Negative Kirkwood--Dirac quasiprobabilities are credited with the quantum advantage of interaction-free measurement and postselected metrology. We test that claim on the task interaction-free measurement was designed for: learning about a sample letting it absorb as little light as possible. The Kirkwood--Dirac distribution of path and output gives the linear response to a weak sample: its real part responds to absorption, its imaginary part to a phase. For a pure single photon passing once through any interferometer, the Fisher information about transmittance per absorbed photon is the direct-transmission value minus a sum of squared imaginary parts: no interferometer or readout beats direct transmission. Negativity plays no role beyond concentrating information in weakly lit outputs. The imaginary parts of the Kirkwood-Dirac distribution depend on the output basis here, not on the sample, so a basis exists in which every term is real, which is optimal. A single photon gains information per absorbed photon only through a phase response, which for an optical line needs a thick or inhomogeneously broadened sample, or through many passes when absorptions go uncounted, as shown by a critically coupled resonator. For detecting a weak absorber, negativity gives a single-shot advantage that does not accumulate over multiple trials; advantage instead accumulates when there are outputs which are dark without the object, a case which needs no negativity.
ER -