We generalize the quantum CUSUM (QUSUM) algorithm for quickest change-point detection, analyzed in finite dimensions by Fanizza, Hirche, and Calsamiglia (Phys. Rev. Lett. 131, 020602, 2023), to infinite-dimensional quantum systems. We employ a novel generalization of Hayashi’s theorem (Hayashi, J. Phys. A: Math. Gen. 34, 3413, 2001) concerning the asymptotics of quantum relative entropy, which we adapt to the infinite-dimensional setting. This enables us to prove that the QUSUM strategy retains its asymptotic optimality, characterized by the relationship between the expected detection delay and the average false alarm time for any pair of states with finite relative entropy. Thus, our findings apply broadly, including continuous-variable systems (e.g., Gaussian states), facilitating the development of optimal change-point detection schemes in quantum optics and other physical platforms, and rendering experimental verification feasible.

Optical pulse position modulation (PPM) places a laser pulse, a.k.a. a coherent state of amplitude$\alpha$of mean photon number$N=\vert \alpha\vert ^{2}$, in one of$M$consecutive time slots, Ideal photon detection on each slot achieves a mean probability of error$((M-1)/1M)e^{-N}$of distinguishing the$iM$PPM codewords, since$e^{-N}$is the probability the pulse-containing slot does not produce a click, per Poisson-shot-noise photo-detection theory. The quantum (Helstrom) limit of the minimum probability of error is lower than above, has a closed-form expression, and scales as$\sim e^{-2N}$when$Me^{-N}\ll 1$. The optimal receiver must make a quantum joint measurement on all$M$slots. Even though receiver algorithms exist that achieve the$\sim e^{-2N}$scaling in the high$N$regime, none are known that bridge the classical-quantum gap for small$N$, the primary regime of interest for optical PPM. It is also not known how close to the Helstrom limit can one get using LOCC. (local operations and classical communications), i.e., a receiver that slices each of the$M$slots into$n$tiny slices, makes a measurement on the first slice, and based on the measurement result picks a measurement to apply to the next slice, etc., until all the$Mn$slices have been measured. In this paper, we propose an LOCC receiver for demodulating PPM that uses semiclassical coherent feedback control and photon detection, which outperforms all known PPM receivers, including one that employed squeezing, a non-classical operation. To bridge the remaining gap to the Helstrom limit, one might need truly quantum operations within a joint (non-LOCC) receiver.

We consider the problem of estimating unknown loss η over$n$uses of single-mode lossy thermal noise bosonic channel under an average photon number constraint per mode. We prove that a product of$n$two-mode squeezed vacuum (TMSV) states achieves minimal quantum Cramér-Rao bound (QCRB) over Gaussian quantum states in this scenario, and characterize the optimal receiver structure. We show that TMSV minimizes QCRB over all quantum states in the limit of low input photon number. Finally, we compare the performance of our optimal receiver for TMSV to other receivers.

We study quantum-secure covert-communication over lossy thermal-noise bosonic channels, the quantum mechanical model for many practical channels. We derive the expressions for the covert capacity of these channels: Lno-EA, when Alice and Bob share only a classical secret, and LEA, when they benefit from entanglement assistance. Entanglement assistance alters the fundamental scaling law for covert communication. Instead of Lno-EA√n-rno-EA(n), rno-EA(n) = o(√n), entanglement assistance allows LEA√n log n - rEA(n), rEA(n) = o(√n log n), covert bits to be transmitted reliably over n channel uses. However, noise in entanglement storage erases the log n gain from our achievability; work on the matching converse is ongoing.

We present a square root law for active sensing of phase θ of a single pixel using optical probes that pass through a single-mode lossy thermal-noise bosonic channel. Specifically, we show that, when the sensor uses an n-mode covert optical probe, the mean squared error (MSE) of the resulting estimator θnscales as 〈(θ-θ̂n)2〉 = O(1/√n) improving the scaling necessarily leads to detection by the adversary with high probability. We fully characterize this limit and show that it is achievable using laser light illumination and a heterodyne receiver, even when the adversary captures every photon that does not return to the sensor and performs arbitrarily complex measurement as permitted by the laws of quantum mechanics.