R. F. Werner. Quantum information theory { an invitation. In Quantum information ( G. Alber et. al., editor), pages 14-59. Springer (2001).  Home/Search   Document Details and Download   Summary   Related Articles   Check

....2. 3 The norm of complete boundedness In many information theoretic studies of noisy quantum channels one needs a quantitative measure of the noisiness of a channel; this is, in fact, a natural departure point for various de nitions of information carrying capacities of quantum channels [15, 18, 36]. A good candidate for such a measure is the norm kT id k , where the question mark refers to the fact that we have not yet speci ed a suitable norm. The choice of the proper norm turns out to be a tricky matter [18] Let A and B be C algebras, and consider a linear map : A B. We cannot ....

....can also be used to characterize completely all ways to write a given T 2 CP(A ; H ) as a nite sum i T i , with T i 2 CP(A ; H ) for all i. It is actually the resulting theorem, stated below, that is referred to as the Radon Nikodym theorem for CP maps in the quantum information literature [36]. Theorem 3.3. Consider a map T 2 CP(A ; H ) with the canonical Stinespring dilation (K ; V; For any nite decomposition T = i T i with T i 2 CP(A ; H ) there exist unique positive operators F i 2 (A ) that satisfy F i = 1K , such that T i (A) V (A) F i V . Proof: ....

R.F. Werner, \Quantum information theory | an invitation," in Quantum Information | an Introduction to Basic Theoretical Concepts and Experiments, Springer Tracts in Modern Physics, vol. 173 (Springer-Verlag, Berlin, 2001), pp. 14-57.

....dissertation. Basic notions of quantum information theory In this chapter we introduce the abstract formalism of quantum information theory. But, before we proceed, it is pertinent to ask: what exactly is quantum information Here is a de nition taken from an excellent survey article of Werner [144]. Quantum information is that kind of information which is carried by quantum systems from the preparation device to the measuring apparatus in a quantummechanical experiment. Of course, this de nition is somewhat vague about the general notion of information, but we can take the pragmatic ....

....are not talking about any quantitative measures of information content. For this reason, such notions as channel capacity will be conspicuously absent form our presentation. For a lucid account of quantum channel capacity, the reader is referred to the surveys of Bennett and Shor [10] and Werner [144]. 2.1 Classical systems vs. quantum systems Classical systems are distinguished from their quantum counterparts through such characteristics as size (macroscopic vs. microscopic) or the nature of their energy spectrum (continuous vs. discrete) For example, an electromagnetic pulse sent through ....

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R.F. Werner, \Quantum information theory | an invitation," in Quantum Information | an Introduction to Basic Theoretical Concepts and Experiments, Springer Tracts in Modern Physics, vol. 173 (Springer-Verlag, Berlin, 2001), pp. 14-57.

....Q(Id) log 2 (d) for the ideal channel. A precise proof of this statement is, however, not so easy as it looks like and we skip the details here. Maybe the most easy approach is to use the quantity log 2 (k Tk cb ) where denotes the transposition) which is an upper bound on Q(T ) cf. 9] or [22]) The same idea can be used to show that the quantum capacity of a classical channel, or more generally a channel T which uses classical information at an intermediate step, is zero. This is a reformulation of the no classical teleportation theorem (cf. again [22] Another useful relation ....

....bound on Q(T ) cf. 9] or [22] The same idea can be used to show that the quantum capacity of a classical channel, or more generally a channel T which uses classical information at an intermediate step, is zero. This is a reformulation of the no classical teleportation theorem (cf. again [22]) Another useful relation concerns the concatenation of two general channels T 1 and T 2 : We transmit quantum information rst through T 1 and then through T 2 . It is reasonable to assume that the capacity of the composition T 2 T 1 can not be bigger than the capacity of the channel with the ....

R. F. Werner. Quantum information theory { an invitation. In Quantum information ( G. Alber et. al., editor), pages 14-59. Springer (2001).

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