QMS Platform is a quantum measurement observability and reconstruction-assurance framework developed to assess whether conclusions drawn from quantum measurement data are supported by the available measurement configuration and reconstruction process. Initial validation is performed using two-qubit photonic tomography. The work evaluates measurement-context normalization, linear state reconstruction, controlled count and background degradation, physical-state projection, maximum-likelihood reconstruction, measurement-context criticality, state-dependent observability, null-space information loss, random-state validation, and the decomposition of structural observability loss from noise propagation. The results establish an initial computational validation baseline while explicitly distinguishing current evidence from broader claims of detector or hardware generality.
QMS Platform is a quantum measurement observability and reconstruction-assurance framework developed to assess whether conclusions drawn from quantum measurement data are supported by the available measurement configuration and reconstruction process. Initial validation is performed using two-qubit photonic tomography. The work evaluates measurement-context normalization, linear state reconstruction, controlled count and background degradation, physical-state projection, maximum-likelihood reconstruction, measurement-context criticality, state-dependent observability, null-space information loss, random-state validation, and the decomposition of structural observability loss from noise propagation. The results establish an initial computational validation baseline while explicitly distinguishing current evidence from broader claims of detector or hardware generality.
The Quantum Measurement Stack (QMS) is an open-source research and software framework for studying what can be inferred about a physical or quantum system from what its detector and measurement architecture make observable. This technical note documents the QMS v0.4.0 Three-Twin Architecture comprising a finite two-mode Gaussian Quantum Twin for observability, reconstruction, estimation and adaptation; a Detector Twin for residual analysis, stage-wise divergence, inverse calibration and mechanism ranking; and a Measurement Twin for causal prediction, innovation analysis, frozen calibration and experimental measurement-state monitoring. Current evidence includes controlled computational validation, same-forward-model CTI parameter recovery using the Pyxel detector-simulation framework, and causal-replay analysis of archival University of Glasgow single-photon experimental measurements. The current evidence does not establish quantum-field reconstruction, general quantum-state tomography, independently validated real-detector calibration, detector-health diagnosis, physical fault attribution, statistically independent physical-event discovery, or prospective experimental validation. The next major milestone is blind external validation using independently configured simulations and held-out experimental measurements.
Drawing inspiration from gradient-descent methods developed for data processing in quantum state tomography [\href{https://iopscience.iop.org/article/10.1088/2058-9565/ae0baa}{Quantum Sci.~Technol.~\textbf{10} 045055 (2025)}] and quantum process tomography [\href{https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.150402}{Phys.~Rev.~Lett.~\textbf{130}, 150402 (2023)}], we introduce stochastic gradient descent (SGD) algorithms for fast quantum measurement tomography (QMT), applicable to both discrete- and continuous-variable quantum systems -- thus completing the tomography trio. A measurement device or detector in a quantum experiment is characterized by a set of positive operator-valued measure (POVM) elements; the goal of QMT is to estimate these operators from experimental data. To ensure physically valid (positive and complete) POVM reconstructions, we propose two distinct parameterization schemes within the SGD framework: one leveraging optimization on a Stiefel manifold and one based on Hermitian operator normalization via eigenvalue scaling. Within the SGD-QMT framework, we further investigate two loss functions: mean squared error, equivalent to L2 or Euclidean norm, and average negative log-likelihood, inspired by maximum likelihood estimation. We benchmark performance against state-of-the-art constrained convex optimization methods. Numerical simulations demonstrate that, compared to standard methods, our SGD-QMT algorithms offer significantly lower computational cost, superior reconstruction fidelity, and enhanced robustness to noise. We make a Python implementation of the SGD-QMT algorithms publicly available at \href{https://github.com/agtomo/SGD-QMT}{github.com/agtomo/SGD-QMT}.
Quantum state tomography (QST) is a crucial technique for characterizing the state of a quantum system. However, the inherent limitations of measurement processes, including detector efficiency and photon counting statistics, introduce noise that affects the accuracy of the reconstructed quantum state. This work presents a rigorous information-theoretic framework for analyzing and quantifying the accuracy achievable in QST. We leverage concepts from information theory, specifically mutual information and channel capacity, to precisely determine the trade-offs between measurement resolution and the complexity of state reconstruction. The central argument is that the achievable accuracy is fundamentally limited by the information that can be reliably extracted from the measurement data, rather than relying solely on empirical estimates of error. This approach provides a theoretical benchmark for evaluating QST protocols and identifying optimal measurement strategies. The key contributions lie in establishing a quantifiable relationship between measurement parameters, noise levels, and the fidelity of the reconstructed quantum state. This offers a more robust and predictive method for assessing the quality of QST than traditional approaches.
Quantum state tomography is a fundamental tool in quantum information processing. It allows us to estimate the state of a quantum system by measuring different observables on many identically prepared copies of the system. This is, in general, a very time-consuming task that requires a large number of measurements. There are, however, systems in which the data acquisition can be done more efficiently. In fact, an ensemble of quantum systems can be prepared and manipulated by external fields while being continuously and collectively probed, producing enough information to estimate its state. This provides a basis for continuous measurement quantum tomography. In this protocol, an ensemble of identically prepared systems is collectively probed and controlled in a time-dependent manner to create an informationally complete continuous measurement record. The measurement history is then inverted to determine the state at the initial time. We use two different estimation methods: maximum likelihood and compressed sensing. The general formalism is applied to the case of reconstruction of the quantum state encoded in the magnetic sub-levels of a large-spin alkali atom, 133Cs. We apply this protocol to the case of reconstruction of states in the full 16-dimensional electronic-ground subspace (F=3⊕F=4), controlled by microwaves and radio-frequency magnetic fields. We present an experimental demonstration of continuous measurement quantum tomography in an ensemble of cold cesium atoms with full control of its 16-dimensional Hilbert space. We show the exquisite level of control achieved in the lab and the excellent agreement between the theory discussed in this dissertation and the experimental results. This allows us to achieve fidelities >95% for low complexity quantum states, and >92% for arbitrary random states, which is a formidable accomplishment for a space of this size.
Quantum state tomography is a fundamental tool in quantum information processing. It allows us to estimate the state of a quantum system by measuring different observables on many identically prepared copies of the system. This is, in general, a very time-consuming task that requires a large number of measurements. There are, however, systems in which the data acquisition can be done more efficiently. In fact, an ensemble of quantum systems can be prepared and manipulated by external fields while being continuously and collectively probed, producing enough information to estimate its state. This provides a basis for continuous measurement quantum tomography. In this protocol, an ensemble of identically prepared systems is collectively probed and controlled in a time-dependent manner to create an informationally complete continuous measurement record. The measurement history is then inverted to determine the state at the initial time. We use two different estimation methods: maximum likelihood and compressed sensing. The general formalism is applied to the case of reconstruction of the quantum state encoded in the magnetic sub-levels of a large-spin alkali atom, 133Cs. We apply this protocol to the case of reconstruction of states in the full 16-dimensional electronic-ground subspace (F=3⊕F=4), controlled by microwaves and radio-frequency magnetic fields. We present an experimental demonstration of continuous measurement quantum tomography in an ensemble of cold cesium atoms with full control of its 16-dimensional Hilbert space. We show the exquisite level of control achieved in the lab and the excellent agreement between the theory discussed in this dissertation and the experimental results. This allows us to achieve fidelities >95% for low complexity quantum states, and >92% for arbitrary random states, which is a formidable accomplishment for a space of this size.
Detector-Plane Causality in Quantum Measurement: A Benchmark Framework for Measurement Integrity and Control This work introduces an instrumentation-level framework for analyzing quantum measurement systems by explicitly localizing irreversible information loss at the detector plane. The detector plane is defined as the combined system consisting of detector materials, front-end electronics, digitization hardware, firmware, and software reconstruction that transform physical detection events into recorded measurement data. The paper proposes the Quantum Measurement Stack (QMS), a causally ordered abstraction that decomposes quantum experiments into operational layers: Field excitation and imprint formation Detector-plane imaging Data acquisition (DAQ) integrity Quantum diagnostics Quantum control system (QCS) Within this framework, the detector plane acts as the effective measurement boundary where correlations can be irreversibly preserved or discarded. To operationalize this concept, the work introduces QMCTB-01, a detector-plane causality benchmark based on a near-field double-slit configuration. The benchmark evaluates two detector regimes under identical photon statistics and propagation conditions: Intensity-only detection, where phase correlations are discarded at the detector plane. Correlation-preserving detection, where phase information is retained through the detector pipeline. Wave-optics simulations demonstrate that interference visibility is determined by detector-plane coherence preservation, not by statistical accumulation of detection events. When correlations are discarded at the detector plane, interference fringes cannot be recovered through averaging, filtering, or post-processing, consistent with established limits of digital signal processing and information theory. The results establish detector-plane coherence fidelity as a measurable instrumentation property and provide a practical benchmark for evaluating detector systems across quantum optics, solid-state detectors, and hybrid quantum platforms. This work frames quantum interference experiments as an instrumentation and signal-processing problem, providing a reproducible methodology for diagnosing detector-induced coherence loss and for designing measurement pipelines that preserve physically relevant correlations. Simulation code and benchmark artifacts supporting this work are available through the associated repository.