Abstract
Quantum tomography has become a key tool for the assessment of quantum states, processes, and devices. This drives the search for tomographic methods that achieve greater accuracy. In the case of mixed states of a single 2-dimensional quantum system adaptive methods have been recently introduced that achieve the theoretical accuracy limit deduced by Hayashi and Gill and Massar. However, accurate estimation of higher-dimensional quantum states remains poorly understood. This is mainly due to the existence of incompatible observables, which makes multiparameter estimation difficult. Here we present an adaptive tomographic method and show through numerical simulations that, after a few iterations, it is asymptotically approaching the fundamental Gill–Massar lower bound for the estimation accuracy of pure quantum states in high dimension. The method is based on a combination of stochastic optimization on the field of the complex numbers and statistical inference, exceeds the accuracy of any mixed-state tomographic method, and can be demonstrated with current experimental capabilities. The proposed method may lead to new developments in quantum metrology.
Highlights
Quantum tomography has become a key tool for the assessment of quantum states, processes, and devices
The basic principles of quantum mechanics strongly limit the processes that can be performed in nature
The method is based on the concatenation of the Complex simultaneous perturbation stochastic approximation (CSPSA), a recently proposed iterative stochastic optimization method on the field of the complex n umbers[30], and Maximum likelihood estimation (MLE), a well known statistical inference m ethod[31]
Summary
Quantum tomography has become a key tool for the assessment of quantum states, processes, and devices. We present an adaptive tomographic method and show through numerical simulations that, after a few iterations, it is asymptotically approaching the fundamental Gill–Massar lower bound for the estimation accuracy of pure quantum states in high dimension. We report an adaptive tomographic method that asymptotically approaches the quantum accuracy limit in the important case of estimating unknown pure quantum states in high dimensions. This is an instance of multi-parameter estimation, where due to the information trade-off among incompatible observables the progress has been slow. The method surpasses the estimation accuracy of any tomographic method designed to estimate mixed states via separable measurements on the ensemble of prepared copies
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