Quantum measurement optimization by decomposition of measurements into extremals

Abstract

Using the convex structure of positive operator value measurements and several quantities used in quantum metrology, such as quantum Fisher information or the quantum Van Trees information, we present an efficient numerical method to find the best strategy allowed by quantum mechanics to estimate a parameter. This method explores extremal measurements thus providing a significant advantage over previously used methods. We exemplify the method for different cost functions in a qubit and in a harmonic oscillator and find a strong numerical advantage when the desired target error is sufficiently small.

Estimation of Gaussian random displacement using non-Gaussian states

“…maximum photon number. Finding the optimal strategy for the case of multiple parameters is generally difficult [25], and is not solved for the displacement problem, even for the well-studied case of no a priori information and no post-selection [12,17,26] (for single-parameter cases, see e.g. [9,22]).…”

Optimal control for Hamiltonian parameter estimation in non-commuting and bipartite quantum dynamics

“…In order to reach the ultimate precision limit set by the physical system, much efforts have been made in the development of standard metrological approaches involving the preparation of optimal probe states [4,[19][20][21][22][23] and the execution of optimal measurements [24][25][26][27][28][29]. It is known that under unitary dynamics, when the whole Hamiltonian takes a multiplicative form of the parameter, H (𝑥) = 𝑥H (as in the case of "phase estimation"), the optimal probe state is of the form (| 𝜆 𝑚𝑎𝑥 + | 𝜆 𝑚𝑖𝑛 )/ √ 2, where | 𝜆 𝑚𝑎𝑥 and | 𝜆 𝑚𝑖𝑛 are eigenvectors of H corresponding to its maximum and minimum eigenvalues [4].…”

Optimal control for Hamiltonian parameter estimation in non-commuting and bipartite quantum dynamics

“…In order to reach the ultimate precision limit set by the physical system, much efforts have been made in the development of standard metrological approaches involving the preparation of optimal probe states [4,[18][19][20][21][22][23] and the execution of optimal measurements [24][25][26][27][28][29]. Using N identical, independent probes, when N is sufficiently large, the error in the estimated value scales as 1/ N in accordance with the central limit theorem.…”