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.
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.
This paper investigates the quickest change detection of quantum states in a universal setting: specifically, where the post-change quantum state is not known a priori. We establish the asymptotic optimality of a two-stage approach in terms of worst average delay to detection. The first stage employs block POVMs with classical outputs that preserve quantum relative entropy to arbitrary precision. The second stage leverages a recently proposed windowed-CUSUM algorithm that is known to be asymptotically optimal for quickest change detection with an unknown post-change distribution in the classical setting.
Modern quantum devices require high-precision Hamiltonian dynamics, but environmental noise can cause calibrated Hamiltonian parameters to drift over time, necessitating expensive recalibration. Detecting when recalibration is needed is challenging, especially since the very gates required for sophisticated verification protocols may themselves be miscalibrated. While cloud quantum computing services implement heuristic routines for triggering recalibration, the fundamental limits of optimal recalibration are not yet known. We develop efficient Hamiltonian certification and changepoint detection protocols in the autonomous setting, where we cannot rely on an external noiseless device and use only single-qubit gates and measurements, making the protocols robust to the calibration issues for multi-qubit operations they aim to detect. For unknown n-qubit Hamiltonians H and H0 with operator norm bounded by M, our certification protocol distinguishes whether ∥H−H0∥F≥ε or ∥H−H0∥F≤O(ε/n) with sample complexity O(nM2ln(1/δ)/ε2) and total evolution time O(nMln(1/δ)/ε2). We achieve this by evolving random stabilizer product states and performing adaptive single-qubit measurements based on a classically simulable hypothesis state. Extending this to continuous monitoring, we develop an online changepoint detection algorithm using the CUSUM procedure that achieves a detection delay time bound of O(nMln(ME∞[T])/ε2), matching the known asymptotically optimal scaling with respect to false alarm run time E∞[T]. Our approach enables quantum devices to autonomously monitor their own calibration status without requiring ancillary systems, entangling operations, or a trusted reference device, offering a practical solution for robust quantum computing with contemporary noisy devices.
This thesis studies quantum-enhanced phase change detection using continuous-variable Gaussian states. The main goal is to understand how different probe states and receiver designs affect the detection of a phase change in a noisy optical channel. The phase change problem is written as a quantum state discrimination problem. The pre-change and post-change states are Gaussian states described by displacement vectors and covariance matrices. A thermal-loss channel is used to model optical loss and background noise, and a phase shift is applied to the signal mode. The main quantum benchmark is the quantum relative entropy (QRE) between the post-change and pre-change states. A pure two-mode Gaussian probe is studied in detail. The probe energy is split between squeezing and coherent displacement. This split is controlled by a power allocation ratio ?. By optimizing over ?, the probe can balance quantum correlations and coherent amplitude under a fixed photon-number constraint. Amplified spontaneous emission (ASE), coherent state, and two-mode squeezed vacuum (TMSV) probes are also considered as comparison cases. Practical receiver designs are then studied using classical relative entropy (CRE). The receivers include ideal photon-number-resolving (PNR) detection, finite-resolution PNR detection, a binary single-photon detector (SPD), an ASE receiver, and a homodyne jointdetection receiver. The finite-resolution study distinguishes binary SPD, with outcomes 0 and ? 1, from 1-PNR, with outcomes 0, 1, and ? 2. The receiver-level classical relative entropy is compared with the quantum relative entropy bound to show how much information each receiver keeps after measurement. Finally, the thesis connects these relative entropy results to the cumulative sum (CUSUM) and quantum CUSUM (QUSUM) frameworks for quickest change detection. In this framework, a larger relative entropy means a shorter detection delay for the same false alarm requirement. The results show that both probe design and receiver design are important for quantum-enhanced phase change detection.
Detecting abrupt changes in data streams is crucial because they are often triggered by events that have important consequences if left unattended. Quickest change-point detection has become a vital sequential analysis primitive that aims at designing procedures that minimize the expected detection delay of a change subject to a bounded expected false alarm time. We put forward the quantum counterpart of this fundamental primitive on streams of quantum data. We give a lower bound on the mean minimum delay when the expected time of a false alarm is asymptotically large, under the most general quantum detection strategy, which is given by a sequence of adaptive collective (potentially weak) measurements on the growing string of quantum data. In addition, we give particular strategies based on repeated measurements on independent blocks of samples that asymptotically attain the lower bound and thereby establish the ultimate quantum limit for quickest change-point detection. Finally, we discuss online change-point detection in quantum channels.
The rapid advancement of quantum information science has spurred research into the ultimate performance limits of quantum systems in communication, sensing, and computation. This thesis adopts a decision-theoretic and information-theoretic viewpoint to systematically study fundamental problems in quantum statistical inference, with a focus on continuous-variable and bosonic platforms. The central theme is to uncover the interplay among physical structure (e.g., Gaussianity and phase-space geometry), operational restrictions (e.g., postselection and covariant measurements), and inference objectives (e.g., risk, error probability, and detection delay), and their joint impact on fundamental limits and attainability. The thesis first advances the understanding of phase-space entropy and the Wigner entropy conjecture. For Wigner-nonnegative quantum states, we develop verifiable sufficient criteria based on moment functionals and purity constraints, thereby extending the range of states for which the conjecture holds. We also establish explicit purity thresholds that guarantee the conjecture in the low-purity regime. These results reveal how Wigner nonnegativity constrains non-Gaussian structure and suggest pathways for incorporating further quantum-realizability conditions. Second, the thesis investigates the role of postselection in quantum state discrimination. We prove that, on average, environment-assisted partial postselection cannot outperform the Helstrom bound, yet conditional improvements are possible in selected branches. This clarifies the decision-theoretic trade-off between conditional performance and success probability, providing a rigorous basis for evaluating postselected protocols. In parameter estimation, we study phase-shift sensing within the covariant measurement framework. By linking the Bayesian risk to the Fourier coefficients of the input state, we derive an explicit characterization of optimal probe states via the Perron–Frobenius theorem and show that Heisenberg scaling is attainable in the high-energy limit. This offers constructive guidance for designing optimal sensing states under symmetry constraints. Finally, the thesis extends classical quickest change detection to sequential quantum inference. We establish the asymptotic relationship between quantum relative entropy and detection delay, and develop protocol architectures tailored to bosonic sensing and joint communication–detection tasks. In particular, for phase-change detection, we provide an analytic framework for computing quantum relative entropy with Gaussian probes, supplying a theoretical toolkit for practical system design. By integrating phase-space methods, information measures, and sequential decision theory, this thesis provides a cohesive analytical framework and delivers several substantive advances in quantum statistical inference for continuous-variable systems, with implications for quantum sensing, quantum communication, and quantum signal processing.
The ability to localize transmission loss change to a subset of links in optical networks is crucial for maintaining network reliability, performance and security. Quantum probes, implemented by sending blocks ofncoherent-state pulses augmented with continuous-variable (CV) squeezing (n=1) or weak temporal-mode entanglement(n>1)over a lossy channel to a receiver with homodyne detection capabilities, are known to be more sensitive than their quasi-classical counterparts in detecting a sudden increase in channel loss. The enhanced sensitivity can be characterized by the increased Kullback-Leibler (KL) divergence of the homodyne output, before and after the loss change occurs. When combined with the theory of quickest change detection (QCD), the increase in KL divergence translates into a decrease in detection latency. In this work, we first revisit quantum probes over a channel, and consider the ratio of quantum to classical KL divergences as a metric for quantum speedup. We generalize previous results onn=1(CV squeezed states) to arbitrary values ofn, and discuss the monotonicity and asymptotics of this ratio with respect to the parameters of the quantum probe. Assuming a subset of nodes in an optical network is capable of sending and receiving such probes through intermediate nodes with all-optical switching capabilities, we present a scheme for quickly detecting the links that have suffered a sudden drop in transmissivity. Since quantum probes lose their sensitivity with increasing loss in the channel, we first propose a probe construction algorithm that makes the set of links suffering transmission loss change identifiable, while minimizing the longest distance a probe traverses. We then introduce new cumulative sum (CUSUM) statistics with a stopping rule, which allows us to run the CUSUM algorithm to quickly localize the faulty links using our constructed probes. Finally, we show that the proposed scheme achieves a quantum speedup in decreasing the localization delay.