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arXiv:2407.13011 · Quantum Science and Technology

Measurement-device agnostic quantum tomography

Robert Stárek, Martin Bielak, Miroslav Ježek

Published Oct 14, 2025• 0 citations
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Abstract

Abstract Characterization of quantum states and devices is paramount to quantum science and technology. The characterization consists of individual measurements, which must be precisely known. A mismatch between actual and assumed constituent measurements limits the accuracy of this characterization. We show that such a mismatch introduces reconstruction artifacts in quantum state tomography. We use these artifacts to detect and quantify the mismatch, gaining information about the actual measurement operators. It consequently allows the mitigation of systematic errors in both quantum measurement and state preparation, improving the precision of state control and characterization. The practical utility of our approach is experimentally demonstrated.

DOI
10.1088/2058-9565/ae1320

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Abstract Characterization of quantum states and devices is paramount to quantum science and technology. The characterization consists of individual measurements, which must be precisely known. A mismatch between actual and assumed constituent measurements limits the accuracy of this characterization. We show that such a mismatch introduces reconstruction artifacts in quantum state tomography. We use these artifacts to detect and quantify the mismatch, gaining information about the actual measurement operators. It consequently allows the mitigation of systematic errors in both quantum measurement and state preparation, improving the precision of state control and characterization. The practical utility of our approach is experimentally demonstrated.
The accurate and reliable description of measurement devices is a central problem in both observing uniquely nonclassical behaviors and realizing quantum technologies from powerful computing to precision metrology. To date quantum tomography is the prevalent tool to characterize quantum detectors. However, such a characterization relies on accurately characterized probe states, rendering reliability of the characterization lost in circular argument. Here we report a self-characterization method of quantum measurements based on reconstructing the response range-the entirety of attainable measurement outcomes, eliminating the reliance on known states. We characterize two representative measurements implemented with photonic setups and obtain fidelities above 99.99% with the conventional tomographic reconstructions. This initiates range-based techniques in characterizing quantum systems and foreshadows novel device-independent protocols of quantum information applications.
Quantum state tomography (QST) is a critical technique for characterizing the state of quantum systems, particularly in the context of quantum computing. Traditional QST protocols rely heavily on precise knowledge of the measurement devices used, introducing significant vulnerabilities to systematic errors and device imperfections. This paper proposes a novel measurement device-independent (MDI) quantum state tomography protocol designed specifically for multi-qubit systems. The core principle of this approach is the strategic utilization of entanglement to minimize the impact of device-specific biases, thereby achieving a more robust and accurate reconstruction of the quantum state. The protocol involves a carefully designed series of measurements performed by multiple, potentially imperfect, measurement devices. Through analyzing the correlations generated by these measurements, we can, with a high degree of certainty, deduce the underlying quantum state without requiring perfect knowledge of each individual device. This MDI QST method represents a significant advancement in overcoming the limitations of conventional QST, paving the way for more reliable and scalable quantum state characterization in complex quantum computing architectures. The theoretical framework and key equations are presented, demonstrating the feasibility and advantages of this approach.
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.
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We show that the information collected in the course of a generic quantum tomography experiment can be used for verifying experimenters' assumptions about the state preparation and measurement. In particular, systematic errors, such as drifts and instabilities inherent in the tomography setup, can be identified without the need for any specific measurements designed to detect such problems. This is done by statistical analysis of available tomography data. As an example, we discuss the detection and characterization of unexpected changes in the signal state preparation during the tomography measurement and argue that minimal tomography schemes, such as symmetric informationally complete measurements, are more difficult to validate than overcomplete schemes. The method is illustrated with the analysis of experimental quantum homodyne tomography.
Estimation of quantum states and measurements is crucial for the implementation of quantum information protocols. The standard method for each is quantum tomography. However, quantum tomography suffers from systematic errors caused by imperfect knowledge of the system. We present a procedure to simultaneously characterize quantum states and measurements that mitigates systematic errors by use of a single high-fidelity state preparation and a limited set of high-fidelity unitary operations. Such states and operations are typical of many state-of-the-art systems. For this situation we design a set of experiments and an optimization algorithm that alternates between maximizing the likelihood with respect to the states and measurements to produce estimates of each. In some cases, the procedure does not enable unique estimation of the states. For these cases, we show how one may identify a set of density matrices compatible with the measurements and use a semi-definite program to place bounds on the state's expectation values. We demonstrate the procedure on data from a simulated experiment with two trapped ions.