On Quantum Statistical Inference, I

Abstract

Recent developments in the mathematical foundations of quantum mechanics have brought the theory closer to that of classical probability and statistics. On the other hand, the unique character of quantum physics sets many of the questions addressed apart from those met classically in stochastics. Furthermore, concurrent advances in experimental techniques and in the theory of quantum computation have led to a strong interest in questions of quantum information, in particular in the sense of the amount of information about unknown parameters in given observational data or accessible through various possible types of measurements. This scenery is outlined (with an audience of statisticians and probabilists in mind).

A shorter version containing some different material will appear (2003), with discussion, in J. Roy. Statist. Soc. B, and is archived as quant-ph/0307191

References in corpus (11)

• Experimental quantum teleportation
• Quantum Nonlocality without Entanglement
• Entanglement-Assisted Classical Capacity of Noisy Quantum Channels
• Maximum-likelihood estimation of the density matrix
• State estimation for large ensembles
• Fisher information in quantum statistics
• Estimating the spectrum of a density operator
• Dynamics of Dissipative Two-Level Systems in the Stochastic Approximation
• Quantum stochastic approach to the description of quantum measurements
• Entanglement-assisted capacity of a quantum channel and the reverse Shannon theorem
• Teleportation into Quantum Statistics

Cited by in corpus (6)

• Measuring Polynomial Invariants of Multi-Party Quantum States
• POVM Quantization
• Seven Principles of Quantum Mechanics
• Quantum theory as a statistical theory under symmetry and complementarity
• On Quantum Statistical Inference, II
• A note on quantum chaology and gamma approximations to eigenvalue spacings for infinite random matrices