Name
Abstract | ||
|---|---|---|
Expressions of several capacity regions in quantum information theory involve an optimization over auxiliary quantum registers. Evaluating such expressions requires bounds on the dimension of the Hilbert space of these auxiliary registers, for which no nontrivial technique is known; we lack a quantum analog of the Carathéodory theorem. In this paper, we develop a new non-Carathéodory-type tool for evaluating expressions involving a single quantum auxiliary register and several classical random variables. As we show, such expressions appear in problems of entanglement-assisted Gray-Wyner and entanglement-assisted channel simulation, where the question of whether entanglement helps in these settings is related to that of evaluating expressions with a single quantum auxiliary register. To evaluate such expressions, we argue that developing a quantum analog of the Carathéodory theorem requires a better understanding of a notion which we call “quantum conditioning.” We then proceed by proving a few results about quantum conditioning, one of which is that quantum conditioning is strictly richer than the usual classical conditioning. |
Year | DOI | Venue |
|---|---|---|
2014 | 10.1109/TIT.2013.2286079 | Information Theory, IEEE Transactions |
Keywords | Field | DocType |
Hilbert spaces,information theory,Carathéodory theorem,Hilbert space,auxiliary quantum systems,entanglement-assisted Gray-Wyner channel simulation,optimization,quantum conditioning,quantum information theory,single quantum auxiliary register,Carathéodory theorem,dimension bound,entanglement assisted classical communication,quantum conditioning | Open quantum system,Discrete mathematics,Combinatorics,Quantum process,Computer science,Quantum algorithm,Quantum information,Quantum operation,Amplitude damping channel,Quantum capacity,Quantum error correction | Journal |
Volume | Issue | ISSN |
60 | 1 | 0018-9448 |
Citations | PageRank | References |
4 | 0.47 | 14 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Salman Beigi | 1 | 56 | 11.43 |
| Amin Gohari | 2 | 144 | 21.81 |