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| Foreword to the second English edition | |
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| Preface to the second Russian edition | |
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| Preface | |
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| Statistical models | |
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| States and measurements | |
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| Some facts about convex sets | |
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| Definition of a statistical model | |
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| The classical statistical model | |
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| Reduction of statistical model. Classical model with a restricted class of measurements | |
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| The statistical model of quantum mechanics | |
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| On the problem of "hidden variables" | |
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| Comments | |
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| Mathematics of quantum theory | |
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| Operators in a Hilbert space | |
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| Quantum states and measurements | |
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| Spectral representation of bounded operators | |
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| Spectral representation of unbounded operators | |
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| On realization of measurement | |
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| Uncertainty relations and compatibility | |
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| Trace-class operators and Hilbert-Schmidt operators | |
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| L2 spaces associated with a quantum state | |
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| Uncertainty relations for measurements with finite second moments | |
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| Matrix representation of square-summable operators. The commutation operator of a state | |
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| Comments | |
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| Symmetry groups in quantum mechanics | |
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| Statistical model and Galilean relativity | |
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| One-parameter shift groups and uncertainty relations | |
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| Kinematics of a quantum particle in one dimension | |
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| Uniqueness theorem. The Schrodinger and the momentum representations | |
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| Minimum-uncertainty states. The completeness relation | |
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| Joint measurements of coordinate and velocity | |
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| Dynamics of a quantum particle in one dimension | |
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| Time observable. The "time-energy" uncertainty relation | |
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| Quantum oscillator and phase measurement | |
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| The coherent-state representation | |
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| Representations of the rotation group and angular momenta | |
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| Measuring the angle of rotation | |
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| Comments | |
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| Covariant measurements and optimality | |
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| Parametric symmetry groups and covariant measurements | |
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| Structure of covariant measurements | |
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| The covariant quantum estimation problem | |
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| Measurements of angular parameters | |
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| Uncertainty relations for angular quantities | |
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| Covariant measurements of angular parameter in the case of arbitrary representation of the group T | |
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| Covariant measurements of a shift parameter | |
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| The case of irreducible representation | |
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| Estimation of pure state | |
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| Measuring parameters of orientation | |
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| Comments | |
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| Gaussian states | |
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| Quasiclassical states of the quantum oscillator | |
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| The CCR for many degrees of freedom | |
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| Proof of the Stone-von Neumann uniqueness theorem. The Weyl transform | |
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| Characteristic function and moments of state | |
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| Structure of general Gaussian states | |
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| A characteristic property of Gaussian states | |
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| Comments | |
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| Unbiased measurements | |
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| Quantum communication channel | |
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| A lower bound for the variance in one-dimensional case | |
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| The case of shift parameter | |
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| Estimation of force by measurements over a trial object | |
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| A bound for the measurement covariance matrix based on symmetric logarithmic derivatives | |
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| A bound based on right logarithmic derivatives | |
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| A general bound for the total mean-square deviation | |
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| Linear measurements | |
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| Mean-value estimation for Gaussian states | |
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| Comments | |
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| Supplement Statistical structure of quantum theory and hidden variables | |
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| Introduction | |
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| The structure of statistical theories | |
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| Axiomatic approaches in quantum mechanics | |
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| The classical picture of statistical experiment | |
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| The main features of statistical description | |
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| Statistical model of quantum mechanics | |
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| Compatibility and complementarity | |
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| Classical and nonclassical models | |
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| The problem of hidden variables | |
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| "No-go" proofs and the minimal statistical requirements on hidden variables | |
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| A hidden variable model for a single quantum system | |
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| Hidden variables and evolutions of quantum system | |
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| Composite systems, EPR paradox and the Bell inequality | |
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| References | |