Limits for molecular spectroscopy from quantum channel discrimination

Abstract

Absorption spectroscopy identifies molecules by detecting frequency-dependent optical loss, and its fundamental limit is a quantum channel-discrimination problem. In this work, we develop a general framework for characterizing the ultimate quantum limit of molecular absorption spectroscopy without collective measurements: we formulate it as an asymmetric quantum hypothesis testing task between different absorption channels. Using a semidefinite-programming formulation, we construct optimal probe states and compare them with coherent-state photon counting, Fock states, and two-mode squeezed vacuum probes. We introduce a random-loss channel model for imperfectly known background transmission, reflecting the fact that a blank experiment need not return all incident photons due to scattering, solvent absorption, or collection losses. Our results show that optimized non-classical probes can substantially outperform conventional laser spectroscopy, and that the advantage is robust to realistic baseline random loss. % In multi-frequency spectroscopy, the optimization also determines how photons should be allocated across absorption lines, revealing an additional resource-allocation advantage beyond single-mode state engineering. We illustrate our framework using infrared detection of 4-nitrophenol against chemically relevant comparison molecules, showing how quantum channel-discrimination methods provide constructive performance limits for molecular spectroscopy under realistic photon constraints.

The paper asks how probe-state and measurement optimization affect photon-constrained molecular absorption detection when collective measurements across interrogations are excluded. It formulates detection as asymmetric discrimination of bosonic loss channels, using channel measured relative entropy $D^M$ as the asymptotic missed-detection error exponent at fixed false-positive tolerance. Baseline attenuation is modelled by an independently redrawn random transmissivity, with additional molecular loss under the alternative hypothesis and weak dephasing under both hypotheses. An existing SDP approximation for $D^M$ is applied to single-frequency sensing and extended to frequency-product probes under a global photon budget. Numerical examples use three infrared features of 4-nitrophenol, with paracetamol and 4-aminophenol as competing hypotheses. Optimized probes outperform the coherent-state photon-counting benchmark; Fock and TMSV probes approach the single-frequency optimum. With baseline transmissivity uniform on $[0.95,1]$, this hierarchy persists. In the three-frequency example with mean photon budget $E=3$ and Fock cutoff $n_{max}=6$, optimization assigns all photons to the $7.407\,\mu\mathrm m$ line; comparison probes receive equal allocations. For composite testing, a shared probe-and-measurement lower bound numerically coincides with the pairwise-optimized upper bound. Photon counting achieves over $90\%$ of the optimized exponent in the tested regime. Limitations include finite Fock truncation, independent baseline fluctuations, and exclusion of frequency-entangled probes. The multifrequency gain combines state optimization with unequal photon allocation. Second-order asymptotics suggest optimized probes become advantageous over Fock/TMSV probes around $n\gtrsim100$ interrogations in one example, but finite-sample optimization remains open.