Basic Notions of Quantum Information

Ángel Luis Plastino, Guido Bellomo, Angel Ricardo Plastino

Nowadays, no one should doubt that quantum entanglement is (at least, one of) the \ncharacteristic traits of quantum mechanics. Furthermore, quantum information science \nis strongly influenced by the advantages provided by quantum entanglement, as the \nlatter can be regarded as a genuine resource for an efficient (better-than-classical) \nprocessing of information in certain computational tasks. The very basic notion of \ncorrelation is fundamental for the conceptualization of the physical communicational \nproblem and, as a consequence, for the notion of information itself. Thus, the question \nabout the nature of quantum information is close (and unavoidably linked) to the \nquestion about the nature of quantum correlations.

Ri‐Gui Zhou, Xiao-Xue Zhang, Lin-Tao Du

M. D. Srinivas

The framework of quantum probability theory is employed in the investigation of ergodic properties of quantum dynamical systems. In the process certain basic notions of quantum information theory are developed. These are used to demonstrate the existence of a quantum Kolmogorov entropy which has the same operational significance as in classical theory. The notion of a quantum K-system is also introduced.

W. D. Heiss

Rossella Lupacchini

In his search for the ‘essence’ of continuity, Richard Dedekind (1872) discovered the notion of cut. Epistemologically speaking, a cut produces a separation of a simply infinite system into two parts (Stücke) such that all the elements of one part are screened off all the elements of the other. The distinct continuity of a two-state quantum system is encapsulated in the notion of qubit, the basic ‘unit’ of quantum information. A qubit secures an infinite amount of information, which, however, appears to be only penetrable through ‘sections’ of classical bits. Whereas Dedekind’s cuts dwell on the discrete of number theory, the theory of nature is primarily concerned with continuous transformations. In contrast with Dedekind’s line of thought, could the notion of information be derived from a ‘principle’ of continuity?