Part I. Fundamental Concepts: 1. Introduction and overview 2. Introduction to quantum mechanics 3. Introduction to computer science Part II. Quantum Computation: 4. Quantum circuits 5. The quantum Fourier transform and its application 6. Quantum search algorithms 7. Quantum computers: physical realization Part III. Quantum Information: 8. Quantum noise and quantum operations 9. Distance measures for quantum information 10. Quantum error-correction 11. Entropy and information 12. Quantum information theory Appendices References Index.

Quantum Computation and Quantum Information

Convergence of Probability Measures. By P. Billingsley. Chichester, Sussex, Wiley, 1968. xii, 253 p. 9 1/4“. 117s.

Convergence of Probability Measures

Fault tolerant quantum computation by anyons

as quantum engineering. In the past two decades it has become increasingly clear that many (perhaps all) of the symptoms of classicality can be induced in quantum systems by their environments. Thus decoherence is caused by the interaction in which the environment in effect monitors certain observables of the system, destroying coherence between the pointer states corresponding to their eigenvalues. This leads to environment-induced superselection or einselection, a quantum process associated with selective loss of information. Einselected pointer states are stable. They can retain correlations with the rest of the universe in spite of the environment. Einselection enforces classicality by imposing an effective ban on the vast majority of the Hilbert space, eliminating especially the flagrantly nonlocal ''Schrodinger-cat states.'' The classical structure of phase space emerges from the quantum Hilbert space in the appropriate macroscopic limit. Combination of einselection with dynamics leads to the idealizations of a point and of a classical trajectory. In measurements, einselection replaces quantum entanglement between the apparatus and the measured system with the classical correlation. Only the preferred pointer observable of the apparatus can store information that has predictive power. When the measured quantum system is microscopic and isolated, this restriction on the predictive utility of its correlations with the macroscopic apparatus results in the effective ''collapse of the wave packet.'' The existential interpretation implied by einselection regards observers as open quantum systems, distinguished only by their ability to acquire, store, and process information. Spreading of the correlations with the effectively classical pointer states throughout the environment allows one to understand ''classical reality'' as a property based on the relatively objective existence of the einselected states. Effectively classical pointer states can be ''found out'' without being re-prepared, e.g, by intercepting the information already present in the environment. The redundancy of the records of pointer states in the environment (which can be thought of as their ''fitness'' in the Darwinian sense) is a measure of their classicality. A new symmetry appears in this setting. Environment-assisted invariance or envariance sheds new light on the nature of ignorance of the state of the system due to quantum correlations with the environment and leads to Born's rules and to reduced density matrices, ultimately justifying basic principles of the program of decoherence and einselection.

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Decoherence, einselection, and the quantum origins of the classical

In information processing, as in physics, our classical world view provides an incomplete approximation to an underlying quantum reality. Quantum effects like interference and entanglement play no direct role in conventional information processing, but they can--in principle now, but probably eventually in practice--be harnessed to break codes, create unbreakable codes, and speed up otherwise intractable computations.

Quantum information and computation

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.

Probabilistic and Statistical Aspects of Quantum Theory

It is shown that the capacity of a classical-quantum channel with arbitrary (possibly mixed) states equals the maximum of the entropy bound with respect to all a priori distributions. This completes the recent result of Hausladen, Jozsa, Schumacher, Westmoreland, and Wootters (1996), who proved the equality for the pure state channel.

The capacity of the quantum channel with general signal states

It is shown that the capacity of a classical-quantum channel with arbitrary (possibly mixed) states equals to the maximum of the entropy bound with respect to all apriori distributions. This completes the recent result of Hausladen, Jozsa, Schumacher, Westmoreland and Wooters, who proved the equality for the pure state channel.

The capacity of quantum channel with general signal states

The Standard Statistical Model of Quantum Mechanics.- Statistics of Quantum Measurements.- Evolution of an Open System.- Repeated and Continuous Measurement Processes.- Processes in Fock Space.

http://www.crm.sns.it/media/course/1406/LECTPISA.pdf

Alexander S. Holevo

Papers

Probabilistic and Statistical Aspects of Quantum Theory

The capacity of the quantum channel with general signal states

The capacity of quantum channel with general signal states

Statistical structure of quantum theory

Statistical decision theory for quantum systems