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arXiv:2104.00652 · Acta Physica Polonica A

Quantum State Tomography of Qutrits by Single-Photon Counting with Imperfect Measurements

Jakub Szlachetka, Artur Czerwiński

Published Sep 1, 2021• 3 citations
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Abstract

In this article, we introduce a framework for quantum state tomography of qutrits by projective measurements.The framework is based on photon-counting with measurement results distorted due to the Poisson noise and dark counts.Two different measurement schemes are investigated numerically and compared in terms of their efficiency for distinct numbers of photons per measurement.The accuracy of state reconstruction is quantified by figures of merit which are presented on graphs versus the amount of noise.

DOI
10.12693/aphyspola.140.210

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In this article, we introduce a framework for quantum state tomography of qutrits by projective measurements.The framework is based on photon-counting with measurement results distorted due to the Poisson noise and dark counts.Two different measurement schemes are investigated numerically and compared in terms of their efficiency for distinct numbers of photons per measurement.The accuracy of state reconstruction is quantified by figures of merit which are presented on graphs versus the amount of noise.
The article undertakes the problem of pure state estimation from projective measurements based on photon counting.Two generic frames for qubit tomography are considered -one composed of the elements of the SIC-POVM and the other defined by the vectors from the mutually unbiased bases.Both frames are combined with the method of least squares in order to reconstruct a sample of input qubits with imperfect measurements.The accuracy of each frame is quantified by the average fidelity and purity.The efficiency of the frames is compared and discussed.The method can be generalized to higher-dimensional states and transferred to other fields where the problem of complex vectors reconstruction appears.
We present a comprehensive framework for quantum state tomography of time-bin qudits sent through a fiber. Starting from basic assumptions, we define a positive-operator valued measure which is then applied to the quantum state reconstruction problem. A realistic scenario is considered where the time uncertainty of the detector is treated as a source of experimental noise. The performance of the quantum tomography framework is examined through a series of numerical simulations conducted for different parameters describing the apparatus. The quality of state recovery, quantified by the notion of minimum fidelity, is depicted on graphs for a range of fiber lengths. Special attention is paid to relative phase reconstruction for qubits and qutrits. The results present relevant interdependence between the fiber length and the detector jitter.
Abstract In this article, we introduce a framework for entanglement characterization by time-resolved single-photon counting with measurement operators defined in the time domain. For a quantum system with unitary dynamics, we generate time-continuous measurements by shifting from the Schrödinger picture to the Heisenberg representation. In particular, we discuss this approach in reference to photonic tomography. To make the measurement scheme realistic, we impose timing uncertainty on photon counts along with the Poisson noise. Then, the framework is tested numerically on quantum tomography of qubits. Next, we investigate the accuracy of the model for polarization-entangled photon pairs. Entanglement detection and precision of state reconstruction are quantified by figures of merit and presented on graphs versus the amount of time uncertainty.
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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.