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.
Journal reference
2026 IEEE International Symposium on Information Theory (ISIT)
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.
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.
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.
Quickest detection of a sudden change in the transmittance of an optical channel is paramount for secure and reliable communications. We show that two-mode squeezed vacuum state, pre-shared between the communicating parties, affords a significant reduction in the quickest-change detection latency compared to when no entanglement is pre-shared: either using a classical coherent-state probe or a quantum-augmented coherent-state that was recently shown to outperform a coherentstate probe. In the absence of thermal noise, the quantum relative entropy (QRE)-whose inverse quantifies the quantum-minimum change-detection latency-is infinite. Even though zero noise and hence instantaneous change detection is unphysical, we show the QRE diverges to infinity as the logarithm of the inverse of the thermal-noise mean photon number. We propose a receiver that achieves the aforesaid QRE scaling, quantify performance improvements over known schemes, and discuss the problem of quantum limits of joint communications and change detection.
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.
Constructing optimal quantum information protocols without complete knowledge of the underlying states or channels is a central challenge. We address this challenge by developing universal correlation detection as a common building block for quantum communication. Our detectors distinguish a bipartite state from the product of its marginals and attain the same first-order asymptotic performance as optimal tests constructed with complete state information. For general bipartite quantum states, knowledge of a single marginal suffices: a detector depending only on that marginal is first-order optimal for every compatible state. For classical-quantum states, the detector is fully universal and requires no prior state information. By combining these detectors with position-based decoding and convex splitting, we construct channel-independent coding schemes that achieve capacity for a range of communication tasks. These results turn universal correlation detection into a systematic tool for universal protocol design, providing a unified route to designing capacity-achieving protocols for many communication tasks over unknown quantum channels.
In the change point problem, we determine when the observed distribution has changed to another one. We expand this problem to a quantum case where copies of an unknown pure state are being distributed. That is, we estimate when the distributed quantum pure state is changed. As the most fundamental case, we treat the problem of deciding the true change point tc between the two given candidates t1 and t2. Our problem is mathematically equal to identifying a given state with one of the two unknown states when multiple copies of the states are provided. The minimum of the averaged error probability is given and the optimal positive operator-valued measure (POVM) is given to obtain it when the initial and final quantum pure states are subject to the invariant prior. We also compute the error probability for deciding the change point under the above POVM when the initial and final quantum pure states are fixed. These analytical results allow us to calculate the value in the asymptotic case.