Adaptive quantum state tomography via linear regression estimation: Theory and two-qubit experiment

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 tomography: Adaptivity improves precisionQuantum state tomography is an essential task in the development of quantum technology. The key problem is to find a strategy that has a high level of estimation accuracy and is easy to experimentally implement. A group of international scientists from China and Australia presented, and experimentally tested, such a strategy, called recursively adaptive quantum state tomography (RAQST). In RAQST, no prior assumption on the state is made. Numerical results show that RAQST, even with the simplest product measurements, outperforms other proposed protocols wherein nonlocal measurements are involved. With error-compensation techniques, the authors experimentally demonstrated its superiority for two-qubit optical tomography. RAQST is particularly effective when reconstructing states with high purity, which are important resources in quantum information. Their method offers a new basis for designing effective approaches for determining a quantum state and can be widely used in quantum information experiments.