Name
Title | ||
|---|---|---|
Constant gap between conventional strategies and those based on C*-dynamics for self-embezzlement |
Abstract | ||
|---|---|---|
We consider a bipartite transformation that we call self-embezzlement and use it to prove a constant gap between the capabilities of two models of quantum information: the conventional model, where bipartite systems are represented by tensor products of Hilbert spaces; and a natural model of quantum information processing for abstract states on C*-algebras, where joint systems are represented by tensor products of C*-algebras. We call this the C*-circuit model and show that it is a special case of the commuting-operator model (in that it can be translated into such a model). For the conventional model, we show that there exists a constant epsilon(0) > 0 such that self-embezzlement cannot be achieved with precision parameter less than epsilon(0) (i.e., the fidelity cannot be greater than 1 - epsilon(0)); whereas, in the C*-circuit model-as well as in a commuting-operator model-the precision can be 0 (i.e., fidelity 1). Self-embezzlement is not a non-local game, hence our results do not impact the celebrated Connes Embedding conjecture. Instead, the significance of these results is to exhibit a reasonably natural quantum information processing problem for which there is a constant gap between the capabilities of the conventional Hilbert space model and the commuting-operator or C*-circuit model. |
Year | DOI | Venue |
|---|---|---|
2022 | 10.22331/q-2022-07-07-755 | QUANTUM |
DocType | Volume | ISSN |
Journal | 6 | 2521-327X |
Citations | PageRank | References |
0 | 0.34 | 0 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Richard Cleve | 1 | 0 | 0.34 |
| Benoit Collins | 2 | 0 | 0.34 |
| Li Liu | 3 | 181 | 12.42 |
| Vern I. Paulsen | 4 | 0 | 0.68 |