The extreme points of \(\mathrm{SU}(2)\)-irreducibly covariant channels. (English) Zbl 1321.81012
Summary: In this paper, we introduce EPOSIC channels, a class of \(\mathrm{SU}(2)\)-covariant quantum channels. For each of them, we give a Kraus representation, its Choi matrix, a complementary channel, and its dual map. We show that they are the extreme points of all \(\mathrm{SU}(2)\)-irreducibly covariant channels. As an application of these channels, we get an example of a positive map that is not completely positive.
MSC:
| 81P45 | Quantum information, communication, networks (quantum-theoretic aspects) |
| 20C35 | Applications of group representations to physics and other areas of science |
| 22E46 | Semisimple Lie groups and their representations |
| 81P68 | Quantum computation |
| 94A40 | Channel models (including quantum) in information and communication theory |
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