Algorithmic complexity of quantum capacity
- 51 Downloads
We analyze the notion of quantum capacity from the perspective of algorithmic (descriptive) complexity. To this end, we resort to the concept of semi-computability in order to describe quantum states and quantum channel maps. We introduce algorithmic entropies (like algorithmic quantum coherent information) and derive relevant properties for them. Then we show that quantum capacity based on semi-computable concept equals the entropy rate of algorithmic coherent information, which in turn equals the standard quantum capacity. Thanks to this, we finally prove that the quantum capacity, for a given semi-computable channel, is limit computable.
KeywordsAlgorithmic complexity Quantum entropies Quantum channels Quantum capacity
- 5.Oskouei, S.K.: Gacs algorithmic complexity in infinite Hilbert spaces and its applications. Ph.D. dissertation, University of Tehran (2015)Google Scholar
- 12.Wolf, M.M., Cubitt, T.S., Perez-Garcia, D.: Are problems in Quantum Information Theory (un)decidable? arxiv.org/abs/1111.5425 (2011)
- 18.Davis, M., Sigal, R., Weyuker, E.J.: Computability, Complexity, and Languages: Fundamentals of Theoretical Computer Science. Academic Press, San Diego (1994)Google Scholar