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Introduction
The state of a physical system is the mathematical description of our knowledge of it, and provides information on its future and past. A state...
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2 Quantum Tomographic Methods
The state of a physical system is the mathematical object that provides a complete information on the system. The knowledge of the state is...
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9 Quantum Operations on Qubitsand Their Characterization
Information encoded in quantum system has to obey rules of quantum physics which impose strict bounds on state estimation and on possible...
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8 Characterization of Quantum Devices
Using quantum tomography and a single entangled state it is possible to characterize completely a quantum device, a channel, or a measuring...
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Method of Invariant Grids
The method of invariant grids is developed for a grid-based computation of invariant manifolds.
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Mathematical Notation and Some Terminology
– The operator L from space W to space E: L : W → E
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Invariance Equation in Differential Form
Definition of invariance in terms of motions and trajectories assumes, at least, existence and uniqueness theorems for solutions of the original...
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Entropy, Quasiequilibrium, and Projectors Field
Projection operators Py contribute both to the invariance equation (3.2), and to the film extension of the dynamics (4.5). Limiting results, exact...
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Geometry of Irreversibility: The Film of Nonequilibrium States
A geometrical framework of nonequilibrium thermodynamics is developed in this chapter. The notion of macroscopically definable ensembles is...
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Film Extension of the Dynamics: Slowness as Stability
One of the difficulties in the problem of reducing the description is caused by the fact that there exists no commonly accepted formal definition of...
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Accuracy Estimation and Post-Processing in Invariant Manifolds Construction
The post-processing algorithms are developed for the accuracy control and enhancement of approximate invariant manifold.
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Method of Natural Projector
P. and T. Ehrenfest introdused in 1911 a model of dynamics with a coarse-graining of the original conservative system in order to introduce...
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Relaxation Methods
The “large step**” relaxation method for solution of the invariance equation is developed.
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Slow Invariant Manifolds for Open Systems
Suppose that the slow invariant manifold is found for a dissipative system. What have we constructed it for? First of all, for solving the Cauchy...
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Quasi-Chemical Representation
In Chap. 5 we have used the second law of thermodynamics, the existence of the entropy, in order to equip the problem of constructing the slow...
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6 Quantum Tomography from Incomplete Data via MaxEnt Principle
We show how the maximum entropy (MaxEnt) principle can be efficiently used for a reconstruction of states of quantum systems from incomplete...
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11 Discrimination of Quantum States
The problem of discriminating among given nonorthogonal quantum states is underlying many of the schemes that have been suggested for quantum...
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12 Quantum States: Discrimination and Classical Information Transmission.A Review of Experimental Progress
The purpose of this chapter is to review the experimental achievements made to date in two closely related areas of quantum information science....
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3 Maximum-Likelihood Methodsin Quantum Mechanics
Maximum Likelihood estimation is a versatile tool covering wide range of applications, but its benefits are apparent particularly in the quantum...