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.
Highlights
One of the central problems in quantum science and technology is the estimation of an unknown quantum state.[1]
We perform the two-qubit state tomography experiments using only the simplest product measurements, and the experimental results demonstrate that the improvement of our recursively adaptive quantum state tomography (RAQST) over nonadaptive tomography is significant for states with a high level of purity
Adaptive linear regression estimation (LRE) A LRE method for Quantum state tomography (QST) was proposed in ref. 6, and the results have shown that the LRE approach has much lower computational complexity than the maximum-likelihood estimation method for quantum tomography
Summary
One of the central problems in quantum science and technology is the estimation of an unknown quantum state.[1]. The development of an efficient data analysis algorithm is a critical issue in QST.[6, 24] In ref.[6], a recursive linear regression estimation (LRE) algorithm was presented which is much more computationally efficient in the sense that it can greatly save the cost of computation as compared to the maximum-likelihood method with only a small amount of accuracy sacrificed This method has even further optimized to fully reconstruct a 14-qubit state within four hours via parallel GPU programming.[25]. We perform the two-qubit state tomography experiments using only the simplest product measurements, and the experimental results demonstrate that the improvement of our RAQST over nonadaptive tomography is significant for states with a high level of purity This limit (very high purity) is the one relevant for most forms of quantum information processing
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