A new proof of the channel coding theorem via hypothesis testing in quantum information theory

A new proof of the direct part of the quantum channel coding theorem is shown based on a standpoint of quantum hypothesis testing. A packing procedure of mutually noncommutative operators is carried out to derive an upper bound on the error probability, which is similar to Feinstein's lemma in classical channel coding. The upper bound is used to show the proof of the direct part along with a variant of Hiai-Petz's theorem in hypothesis testing.

[1]  M. Hayashi,et al.  On error exponents in quantum hypothesis testing , 2002, IEEE Transactions on Information Theory.

[2]  Masahito Hayashi,et al.  General formulas for capacity of classical-quantum channels , 2003, IEEE Transactions on Information Theory.

[3]  Hiroki Koga,et al.  Information-Spectrum Methods in Information Theory , 2002 .

[4]  M. Hayashi.  Optimal sequence of POVMs in the sense of Stein's lemma in quantum hypothesis testing , 2001, quant-ph/0107004.

[5]  H. Nagaoka,et al.  Strong converse and Stein's lemma in quantum hypothesis testing , 1999, IEEE Trans. Inf. Theory.

[6]  Andreas J. Winter,et al.  Coding theorem and strong converse for quantum channels , 1999, IEEE Trans. Inf. Theory.

[7]  Akio Fujiwara,et al.  Operational Capacity and Pseudoclassicality of a Quantum Channel , 1998, IEEE Trans. Inf. Theory.

[8]  Alexander S. Holevo,et al.  The Capacity of the Quantum Channel with General Signal States , 1996, IEEE Trans. Inf. Theory.

[9]  Michael D. Westmoreland,et al.  Sending classical information via noisy quantum channels , 1997 .

[10]  Schumacher,et al.  Classical information capacity of a quantum channel. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[11]  Sergio Verdú,et al.  A general formula for channel capacity , 1994, IEEE Trans. Inf. Theory.

[12]  F. Hiai,et al.  The proper formula for relative entropy and its asymptotics in quantum probability , 1991 .

[13]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[14]  A. S. Holevo,et al.  Capacity of a quantum communication channel , 1979 .

[15]  A. Uhlmann.  Relative entropy and the Wigner-Yanase-Dyson-Lieb concavity in an interpolation theory , 1977 .

[16]  G. Lindblad.  Completely positive maps and entropy inequalities , 1975 .

[17]  L. Goddard.  Information Theory , 1962, Nature.

[18]  D. Blackwell,et al.  The Capacity of a Class of Channels , 1959 .

[19]  J. Wolfowitz.  The coding of messages subject to chance errors , 1957 .

[20]  Amiel Feinstein,et al.  A new basic theorem of information theory , 1954, Trans. IRE Prof. Group Inf. Theory.