Quantum information theory

C. Macchiavello, G. M. Palma, and A. Zeilinger, Quantum Computation and Quantum Information Theory, World Scientific, 2000. 

Rissler, J., Noack, R.M., White, S.R. Measuring orbital interaction using quantum information theory. Chem. Phys. 2006, 323(2-3), 519. 

Braunstein S. L. and Pati A. K., Quantum Information Theory with Continuous Variables, (Kluwer, Dordrecht, 2003), and references therein. 

The first prototype of quantum cryptographic apparatus came into existence around 1990 [147]. In the meantime, quantum cryptography has become a well-known technique of communication in a provably secure way, and together with an intensive research in the held of quantum computers it has given rise to a whole new branch of science quantum information theory [148]. Viewed from this perspective, quantum cryptography today is only a subset of a broad held of quantum communications that also include quantum teleportation, quantum dense coding, quantum error-correcting codes, and quantum data compression. 

Theoretical predictions of decoherence rates, based on known interactions between system and environment, are still only at a primitive level due to the complexity of most experimental situations. A simple example will be discussed in this chapter in relation to one of the experiments. The Compton scattering of neutrons also seems to allow measurements that have another connection to recent discussions on quantum information theory, namely, the energy needed to destroy information stored in quantum entanglement. At the end of this chapter, this possibility will be mentioned briefiy. 

V0I.712 W. Potz, J. Fabian, U. Hohenester (Eds.), Modem Aspects of Spin Physics V0I.713 L. Diosi, A Short Course in Quantum Information Theory... 

A third hint of a connection between physics and information theory comes from the thermodynamics of Black Holes, which is still a deep mystery that embodies principles from quantum mechanics, statistical mechanics and general relativity. 

An analogous role has been played by other scientists in strengthening the ties between quantum chemistry of type I (and type II) with the area corresponding to biochemistry (or complex molecular systems in general), a task made more difficult by the explosive growth of structural and functional information about biomolecular systems. It is worth to remark here that such a fruitful use of quantum chemical concepts in biology has requested the extension of the methods to approaches different from quantum molecular theory in the strict sense introduced before. We shall comeA back to this remark later. 

The main objective of the Workshop was to bring together people working in areas of Fundamental physics relating to Quantum Field Theory, Finite Temperature Field theory and their applications to problems in particle physics, phase transitions and overlap regions with the areas of Quantum Chaos. The other important area is related to aspects of Non-Linear Dynamics which has been considered with the topic of chaology. The applications of such techniques are to mesoscopic systems, nanostructures, quantum information, particle physics and cosmology. All this forms a very rich area to review critically and then find aspects that still need careful consideration with possible new developments to find appropriate solutions. 

To illustrate an application of nonlinear quantum dynamics, we now consider real-time control of quantum dynamical systems. Feedback control is essential for the operation of complex engineered systems, such as aircraft and industrial plants. As active manipulation and engineering of quantum systems becomes routine, quantum feedback control is expected to play a key role in applications such as precision measurement and quantum information processing. The primary difference between the quantum and classical situations, aside from dynamical differences, is the active nature of quantum measurements. As an example, in classical theory the more information one extracts from a system, the better one is potentially able to control it, but, due to backaction, this no longer holds true quantum mechanically. 

Flow can one make practical use of these observations For some time I have advocated the use of information theory. (For more details see introductory discussions in Refs. [1] and [3], surprisal analysis in Ref. [23], applications to spectra in Refs. [24] and [30], and a recent prediction of a phase transition induced by cluster impact in Ref. [31]). What this approach seeks to do is to use the minimal dynamical input that is necessary to account for the dynamical observations of interest, the point being that one very rarely has the experimental resolution to probe the individual final quantum states. The information measured is much more coarse grained. 

As has long been known, every derivation of the bulk properties of matter from its atomic properties by statistical methods encounters essential difficulties of principle. Their effect is that in all but the simplest cases (i.e., equilibrium) the development does not take the form of a deductive science. This contrasts with the usual situation in physics e.g., Newtonian or relativistic mechanics, electromagnetism, quantum theory, etc. The present paper, after focusing on this difficulty, seeks a way out by exploring the properties of a special class of statistical kinetics to be called relaxed motion and to be defined by methods of generalized information theory. 

Modern Information Theory is based on the invaricntivc double density functional f p(x) log [p(x)iq(x) dx. In classical or quantum mechanics a basic time-independent q(x) exists. In the case considered here, q(x) = 1 by Liouville s theorem. Cf S. Kullback, Information Theory and Statistics, Wiley, New York, 1959. 

The general theory for the absorption of light and its extension to photodissociation is outlined in Chapter 2. Chapters 3-5 summarize the basic theoretical tools, namely the time-independent and the time-dependent quantum mechanical theories as well as the classical trajectory picture of photodissociation. The two fundamental types of photofragmentation — direct and indirect photodissociation — will be elucidated in Chapters 6 and 7, and in Chapter 8 I will focus attention on some intermediate cases, which are neither truly direct nor indirect. Chapters 9-11 consider in detail the internal quantum state distributions of the fragment molecules which contain a wealth of information on the dissociation dynamics. Some related and more advanced topics such as the dissociation of van der Waals molecules, dissociation of vibrationally excited molecules, emission during dissociation, and nonadiabatic effects are discussed in Chapters 12-15. Finally, we consider briefly in Chapter 16 the most recent class of experiments, i.e., the photodissociation with laser pulses in the femtosecond range, which allows the study of the evolution of the molecular system in real time. 

Tremendous progress has been made in the fundamental theory of quantum information and there is currently a global race to find a practical technology for quantum computing. Quantum computation is potentially the most innovative area that can be addressed within nanotechnology, embracing nanofabrication and molecular nanotechnology, as well as atomic and molecular manipulation and assembly. 

Many semi-classical and quantum mechanical calculations have been performed on the F + H2 reaction, mainly being restricted to one dimension [520, 521, 602]. The prediction of features due to quantum-mechanical interferences (resonances) dominates many of the calculations. In one semi-classical study [522], it was predicted that the rate coefficient for the reaction F (2P1/2) + H2 is about an order of magnitude smaller than that for F(2P3/2) 4- H2, which lends support to the conclusion [508] that the experimental studies relate solely to the reaction of ground state fluorine atoms. Information theory has been applied to many aspects of the reaction including the rotational energy disposal and branching ratios for F + HD [523, 524] and has been used for transformation of one-dimensional quantum results to three dimensions [150]. Linear surprisal plots occur for F 4- H2(i> = 0), as noted before, but non-linear surprisal plots are noted in calculations for F + H2 (v < 2) [524],... 

D. Bonchev, N. Trinajstic, Chemical Information Theory Structural Aspects, Intern. J. Quantum. Chem. Symp., 18 (1982) 463-480. 

In this paper, we have reviewed the main methods currently used to protect quantum information from the effects of the environment we have presented the general idea of quantum error-correction as well as the formal theory which has recently emerged. Moreover, we have briefly introduced the most impor-... 

Preskill J., Lecture Notes for Physics 229 Quantum Information and Computation, (California Institute of Technology, 1998), http //www.theory.caltech.edu/ preskill/ph229. 

The major advance of the past decade is that, using quantum-chemical computations, activation energies (Eact) as well as activation entropies (AS ) can be predicted a priori for systems of catalytic interest. This implies much more reliable use of the transition-state reaction rate expression than before, since no assumption of the transition state-structure is necessary. This transition-state structure can now be predicted. However, the estimated absolute accuracy of computed transition states is approximately of the order of 20-30 kJ/mol. Here, we do not provide an extensive introduction to modern quantum-chemical theory that has led to this state of affairs excellent introductions can be found elsewhere [38,39]. Instead, we use the results of these techniques to provide structural and energetic information on catalytic intermediates and transition states. 

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