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IEEE Journal on Selected Areas in Communications

Adaptive Quantum State Tomography

Phillip Cornett, Albert B. Dinkins V, Kwang‐Cheng Chen

Published Jan 1, 2026• 0 citations
Publisher
DOI
10.1109/jsac.2026.3737733

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Abstract Adaptive techniques have great potential for wide application in enhancing the precision of quantum parameter estimation. We present an adaptive quantum state tomography protocol for finite dimensional quantum systems and experimentally implement the adaptive tomography protocol on two-qubit systems. In this adaptive quantum state tomography protocol, an adaptive measurement strategy and a recursive linear regression estimation algorithm are performed. Numerical results show that our adaptive quantum state tomography protocol can outperform tomography protocols using mutually unbiased bases and the two-stage mutually unbiased bases adaptive strategy, even with the simplest product measurements. When nonlocal measurements are available, our adaptive quantum state tomography can beat the Gill–Massar bound for a wide range of quantum states with a modest number of copies. We use only the simplest product measurements to implement two-qubit tomography experiments. In the experiments, we use error-compensation techniques to tackle systematic error due to misalignments and imperfection of wave plates, and achieve about a 100-fold reduction of the systematic error. The experimental results demonstrate that the improvement of adaptive quantum state tomography over nonadaptive tomography is significant for states with a high level of purity. Our results also show that this adaptive tomography method is particularly effective for the reconstruction of maximally entangled states, which are important resources in quantum information.
Quantum state tomography strategy via weak value is valid for arbitrary dimensional systems, and can be easily realized. However, the efficiency of quantum state tomography strategy via weak value is lower than that of the conventional quantum state tomography (QST), especially for high-dimensional systems. To improve the efficiency of the scheme, we propose a two-step adaptive quantum state tomography via weak value for pure states (AQSTW). In AQSTW, by using appropriate measurement strength, the efficiency of AQSTW is significantly larger than that of the conventional QST, especially for high-dimensional systems. And AQSTW can be easily implemented. These results demonstrate AQSTW may be useful in the measurements of the unknown quantum states.