No 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.

No abstract

No abstract

Current noise levels in physical realizations of qubits and quantum operations limit the applicability of conventional methods to characterize entanglement. In this adverse scenario, we follow a quantum variational approach to estimate the geometric measure of entanglement of multiqubit pure states. The algorithm requires only single-qubit gates and measurements, so it is well suited for noisy intermediatescale quantum devices. This is demonstrated by successfully implementing the method on IBM Quantum devices for Greenberger-Horne-Zeilinger states of three, four, and five qubits. Numerical simulations with random states show the robustness and accuracy of the method. The scalability of the protocol is numerically demonstrated via matrix-product-state techniques up to 25 qubits.