Experiment design and parameter estimation of Pauli channels using convex optimization

Abstract

A unified framework is proposed in this paper for parameter estimation using convex optimization and experiment design applying convex maximization for Pauli channels, that can be extended to generalized Pauli channels, too. In the case of known channel directions, an affine parametrization of the Choi matrix turns the LS parameter estimation into a convex optimization problem also for the generalized Pauli channels. A simple iterative algorithm for estimating the channel directions is also given for qubit Pauli channels. The experiment design was performed by maximizing the trace of the Fisher information matrix of the output quantum system to find optimal input state and measurement POVM for the channel estimation. For the known channel direction case it was found that the optimal input state should be pure and the optimal measurement POVM is extremal. It was also shown that both the input state and the POVM elements in the optimal configuration should be parallel to the channel directions in the qubit Pauli channel case. The proposed methods and algorithms are illustrated by simple numerical examples.

References in corpus (14)

• Experimental Quantum State Tomography of Optical Fields and Ultrafast Statistical Sampling
• Unknown Quantum States and Operations, a Bayesian View
• Quantum Process Tomography: Resource Analysis of Different Strategies
• State estimation for large ensembles
• Minimal qubit tomography
• Classical randomness in quantum measurements
• Optimizing Completely Positive Maps using Semidefinite Programming
• Maximum-likelihood reconstruction of CP maps
• Optimal parameter estimation of depolarizing channel
• Simplified Quantum Process Tomography
• Optimal experiment design revisited: fair, precise and minimal tomography
• Optimal quantum multi-parameter estimation and application to dipole- and exchange-coupled qubits
• Optimal Experiment Design for Quantum State and Process Tomography and Hamiltonian Parameter Estimation
• Parameter estimation of quantum processes using convex optimization