Reliable and efficient reconstruction of pure quantum states under the processing of noisy measurement data is a vital tool in fundamental and applied quantum information sciences owing to communication, sensing, and computing. Specifically, the purity of such reconstructed quantum systems is crucial in surpassing the classical shot-noise limit and achieving the Heisenberg limit, regarding the achievable precision in quantum sensing. However, the noisy reconstruction of such resourceful sensing probes limits the quantum advantage in precise quantum sensing. For this, we formulate a pure quantum state reconstruction method through eigenvalue decomposition. We show that the proposed method is robust against the depolarizing noise; it remains unaffected under high strength white noise and achieves quantum state reconstruction accuracy similar to the noiseless case.
Reliable and efficient reconstruction of pure quantum states under the processing of noisy measurement data is a vital tool in fundamental and applied quantum information sciences owing to communication, sensing, and computing. Specifically, the purity of such reconstructed quantum systems is crucial in surpassing the classical shot-noise limit and achieving the Heisenberg limit, regarding the achievable precision in quantum sensing. However, the noisy reconstruction of such resourceful sensing probes limits the quantum advantage in precise quantum sensing. For this, we formulate a pure quantum state reconstruction method through eigenvalue decomposition. We show that the proposed method is robust against the depolarizing noise; it remains unaffected under high strength white noise and achieves quantum state reconstruction accuracy similar to the noiseless case.
Abstract The reliable characterization of quantum states as well as any potential noise in various quantum systems is crucial for advancing quantum technologies. In this work we propose the concept of corrupted sensing quantum state tomography which enables the simultaneous reconstruction of quantum states and structured noise with the aid of simple Pauli measurements only. Without additional prior information, we investigate the reliability and robustness of the framework. The power of our protocol is demonstrated by assuming sparse Gaussian and Poisson noise for low-rank state tomography. In particular, our approach is able to achieve a high quality of the recovery with incomplete sets of measurements and is also suitable for performance improvement of large quantum systems. It is envisaged that the techniques can become a practical tool to greatly reduce the cost and computational effort for quantum tomography in noisy quantum systems.
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.
In quantum information transformation and quantum computation, the most critical issues are security and accuracy. These features, therefore, stimulate research on quantum state characterization. A characterization tool, Quantum state tomography, reconstructs the density matrix of an unknown quantum state. Theoretically, reconstructing an unknown state using this method can be arbitrarily accurate. However, this is less practical owing to the huge burden of measurements and data processing for large numbers of qubits. Even comprising an efficient estimator and a precise algorithm, an optimal tomographic framework can also be overburdened owing to the exponential growth of the measurements. Moreover, the consequential postprocessing of huge amounts of data challenges the capacity of computers. Thus, it is crucial to build an efficient framework that requires fewer measurements but yields an expected accuracy. To this end, we built a tomography schema by which only a few Pauli measurements enable an accurate tomographic reconstruction. Subsequently, this schema was verified as efficient and accurate through numerical simulations on the tomography of multi-qubit quantum states. Furthermore, this schema was proven to be robust through numerical simulations on a noisy superconducting qubit system. Therefore, the tomography schema paves an alternatively effective way to reconstruct the density matrix of a quantum state owing to its efficiency and accuracy, which are essential for quantum state tomography.
Quantum state tomography (QST) is a fundamental technique in quantum information science, aiming to reconstruct the density matrix of an unknown quantum state from experimental measurements. However, traditional QST methods often suffer from significant computational demands and are highly susceptible to measurement noise, hindering their practical application, particularly with near-term quantum computers. This work proposes a novel approach to QST utilizing variational quantum algorithms (VQAs). VQAs iteratively optimize a parameterized quantum circuit to minimize a cost function related to the fidelity between the desired state and the state predicted by the circuit. This approach dramatically reduces the number of required measurements and offers the potential for achieving high-fidelity state reconstruction with lower quantum resource requirements. We detail the theoretical framework, outlining the core algorithms and mathematical formulations. The key advantage lies in the ability to learn the state directly, mitigating the limitations of traditional methods. We explore the optimization landscape and discuss strategies for improving convergence and robustness. The results demonstrate a promising path toward scalable and robust QST on quantum devices.
In the light of the progress in quantum technologies, the task of verifying the correct functioning of processes and obtaining accurate tomographic information about quantum states becomes increasingly important. Compressed sensing, a machinery derived from the theory of signal processing, has emerged as a feasible tool to perform robust and significantly more resource-economical quantum state tomography for intermediate-sized quantum systems. In this work, we provide a comprehensive analysis of compressed sensing tomography in the regime in which tomographically complete data is available with reliable statistics from experimental observations of a multi-mode photonic architecture. Due to the fact that the data is known with high statistical significance, we are in a position to systematically explore the quality of reconstruction depending on the number of employed measurement settings, randomly selected from the complete set of data, and on different model assumptions. We present and test a complete prescription to perform efficient compressed sensing and are able to reliably use notions of model selection and cross validation to account for experimental imperfections and finite counting statistics. Thus, we establish compressed sensing as an effective tool for quantum state tomography, specifically suited for photonic systems.
The development of large-scale platforms for quantum information requires new methods for verification and validation of quantum behavior. Quantum tomography (QT) is the standard tool for diagnosing quantum states, process, and readout devices by providing complete information. However, QT is limited since it is expensive to not only implement experimentally, but also requires heavy classical post-processing of data. In this dissertation, we introduce new methods for QT that are more efficient to implement and robust to noise and errors, thereby making QT a more practical tool for current quantum information experiments. The crucial detail that makes these new, efficient, and robust methods possible is prior information about the quantum system. This prior information is prompted by the goals of most experiments in quantum information, which require pure states, unitary processes, and rank-1 POVM operators. Therefore, most experiments are designed to operate near this ideal regime. We show that when this is the case, QT can be accomplished with significantly fewer resources, and produce a robust estimate in the presence of noise and errors. Moreover, the estimate is also robust if the state is not exactly pure, the process is not exactly unitary, or the POVM is not exactly rank-1. Such compelling methods are only made possible by the positivity constraint on quantum states, processes, and POVMs. This requirement is an inherent feature of quantum mechanics, but has powerful consequences to QT. Since QT is necessarily an experimental tool, we discuss a test of these new methods in an experimental setting. The physical system is an ensemble of laser-cooled cesium atoms in the laboratory of Prof. Poul Jessen. Experiments were conducted by Hector Sosa-Martinez et al. to demonstrate different QT protocols. We compare the results, and conclude that the new methods are effective.