Estimation of pure quantum states in high dimension at the limit of quantum accuracy through complex optimization and statistical inference

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.

Entangled spintronic modulated high‐performance Ce 2 O 3 small polaron surface state‐based water splitting cells

“…Unfortunately, an accurate estimate quantum state still keeps the difficulty since the compatible observables or devices are not exist. 37 An adaptive tomographic method is therefore been provided through numerical simulations, which got the highest accuracy tomographic method when it is based on stochastic optimization and statistical inference. 37 To address these issues, first, the entangled spintronic are excited from Ce 2 O 3 small polaron state by ħ + ħ (""), ħ + (−ħ) (#"), ħ -(−ħ) ("#), and (−ħ) + (−ħ) (##) angular momentum modulated light irradiation, which is utilized to raise the performance of Ce 2 O 3 small polaron water splitting cells.…”

“…37 An adaptive tomographic method is therefore been provided through numerical simulations, which got the highest accuracy tomographic method when it is based on stochastic optimization and statistical inference. 37 To address these issues, first, the entangled spintronic are excited from Ce 2 O 3 small polaron state by ħ + ħ (""), ħ + (−ħ) (#"), ħ -(−ħ) ("#), and (−ħ) + (−ħ) (##) angular momentum modulated light irradiation, which is utilized to raise the performance of Ce 2 O 3 small polaron water splitting cells. Second, we provide an attempt for decrypting entangled spintronic from Ce 2 O 3 small polaron surface state via tomography by defined quantum states for spintronic current.…”

“…Quantum computing is always seen as confident processing for managing computational tasks. Unfortunately, an accurate estimate quantum state still keeps the difficulty since the compatible observables or devices are not exist 37 . An adaptive tomographic method is therefore been provided through numerical simulations, which got the highest accuracy tomographic method when it is based on stochastic optimization and statistical inference 37 …”

Quantum State Tomography of Four-Level Systems with Noisy Measurements

“…More specifically, we investigate the problem of QST of four-level systems described by pure states. Reconstruction of pure states (or almost pure) usually involves separate tomographic techniques [20][21][22]. In our scheme, two generic frames are applied in order to reconstruct a sample of 4−dimensional complex vectors.…”

High-accuracy adaptive quantum tomography for high-dimensional quantum systems

“…In particular, we introduce a method for high-accuracy quantum tomography (HAQT) that is based on the strategy of adaptive projective measurements. Measurement adaptation [17] has been suggested as a means to increase the estimation accuracy of tomographic schemes [18][19][20][21][22][23]. In the case of d = 2, adaptive quantum tomography (AQT) [24] reaches the optimal estimation accuracy given by the Gill-Massar lower bound [25].…”