# Probabilistic and Statistical Aspects of Quantum Theory

@inproceedings{Holevo1982ProbabilisticAS, title={Probabilistic and Statistical Aspects of Quantum Theory}, author={Alexander S. Holevo and Leslie Ballentine}, year={1982} }

Foreword to 2nd English edition.- Foreword to 2nd Russian edition.- Preface.- Chapters: I. Statistical Models.- II. Mathematics of Quantum Theory.- III. Symmetry Groups in Quantum Mechanics.- IV. Covariant Measurements and Optimality.- V. Gaussian States.- VI Unbiased Measurements.- Supplement - Statistical Structure of Quantum Theory and Hidden Variables.- References.

## 2,385 Citations

### Foundations of Quantum Mechanics, an Empiricist Approach

- Physics
- 2002

Preface. 1. Standard and generalized formalisms of quantum mechanics. 2. Empiricist and realist interpretations of quantum mechanics. 3. Quantum mechanical description of measurement, and the…

### On quantum statistical inference

- Mathematics
- 2003

Summary. Interest in problems of statistical inference connected to measurements of quantum systems has recently increased substantially, in step with dramatic new developments in experimental…

### Quantum theory: the role of microsystems and macrosystems

- Physics
- 2007

We stress the notion of statistical experiment, which is mandatory for quantum mechanics, and recall Ludwig's foundation of quantum mechanics, which provides the most general framework to deal with…

### The structure of classical extensions of quantum probability theory

- Mathematics
- 2008

On the basis of a suggestive definition of a classical extension of quantum mechanics in terms of statistical models, we prove that every such classical extension is essentially given by the…

### Bell-type Models and Statistical Description of Quantum Systems

- Physics
- 2008

We consider dynamics of hidden variables for measurements in a generalized bell-type model for a single spin using natural assumptions. The evolution of the system, which can be expressed as dynamic…

### Statistical Model with Measurement Degree of Freedom and Quantum Physics

- Physics
- 2003

This is an English translation of the manuscript which appeared in Surikaiseki Kenkyusho Kokyuroku No. 1055 (1998). The asymptotic efficiency of statistical estimate of unknown quantum states is…

### Uhlmann's parallelism in quantum estimation theory

- Physics
- 1997

Two important classes of the quantum statistical model, the locally quasi-classical model and the quasi-classical model, are introduced from the estimation theoretical viewpoint, and they are…

### Quantum mechanics for probabilists

- Physics
- 2021

Many topics of modern probability have counterparts in mathematical physics and quantum mechanics. For example, the study of the parabolic Anderson model is related to Anderson localization;…

### Basics of Quantum Mechanics

- Physics
- 2011

Quantum mechanics was started after works by Heisenberg (Z. Phys. 43:172, 1927), Schrodinger (Naturwissenschaften 48:52, 1935) and Dirac around 1925. Together with relativity theory it is the most…

### Geometry of Quantum Statistical Inference.

- Physics, MathematicsPhysical review letters
- 1996

An efficient geometric formulation of the problem of parameter estimation is developed, based on Hilbert space geometry, and a set of higher order corrections to the parameter estimation variance lower bound are found, which are potentially important in quantum mechanics.