Quantum process tomography via optimal design of experiments

Abstract

Quantum process tomography --- a primitive in many quantum information processing tasks --- can be cast within the framework of the theory of design of experiment (DoE), a branch of classical statistics that deals with the relationship between inputs and outputs of an experimental setup. Such a link potentially gives access to the many ideas of the rich subject of classical DoE for use in quantum problems. The classical techniques from DoE cannot, however, be directly applied to the quantum process tomography due to the basic structural differences between the classical and quantum estimation problems. Here, we properly formulate quantum process tomography as a DoE problem, and examine several examples to illustrate the link and the methods. In particular, we discuss the common issue of nuisance parameters, and point out interesting features in the quantum problem absent in the usual classical setting.

18 pages, 4 figures

References in corpus (1)

• Adaptive experimental design for one-qubit state estimation with finite data based on a statistical update criterion

Cited by in corpus (10)

• A perspective on multiparameter quantum metrology: from theoretical tools to applications in quantum imaging
• Learning Quantum Systems
• Quantum state estimation with nuisance parameters
• One from many: Estimating a function of many parameters
• Nuisance parameter problem in quantum estimation theory: General formulation and qubit examples
• Active Learning of Quantum System Hamiltonians yields Query Advantage
• Proof-of-principle experimental demonstration of quantum gate verification
• Quantum-state estimation problem via optimal design of experiments
• Quantum Active Learning
• Heisenberg-scaling characterization of a two-channel optical network via two-port homodyne detection