Universal approximation of multi-copy states and universal quantum lossless data compression

We have proven that there exists a quantum state approximating any multi-copy state universally when we measure the error by means of the normalized relative entropy. While the qubit case was proven by Krattenthaler and Slater (IEEE Trans. IT, 46, 801-819 (2000); quant-ph/9612043), the general case has been open for more than ten years. For a deeper analysis, we have solved the mini-max problem concerning `approximation error' up to the second order. Furthermore, we have applied this result to quantum lossless data compression, and have constructed a universal quantum lossless data compression

Universal coding for classical-quantum channel

We construct a universal code for stationary and memoryless classical-quantum channel as a quantum version of the universal coding by Csisz\'{a}r and K\"{o}rner. Our code is constructed by the combination of irreducible representation, the decoder introduced through quantum information spectrum, and the packing lemma

Mouse Chromosome 3

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46995/1/335_2004_Article_BF00648421.pd

Elimination of correlation in random codes for arbitrarily varying channels

Ahlswede R. Elimination of correlation in random codes for arbitrarily varying channels. Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete. 1978;44(2):159-175.The author determines for arbitrarily varying channels a) the average error capacity and b) the maximal error capacity in case of randomized encoding. A formula for the average error capacity in case of randomized encoding was announced several years ago by Dobrushin ([3]). Under a mild regularity condition this formula turns out to be valid and follows as consequence from either a) or b)