## Quantum Communication Complexity of Symmetric Predicates (2002)

Venue: | Izvestiya of the Russian Academy of Science, Mathematics |

Citations: | 87 - 1 self |

### BibTeX

@ARTICLE{Razborov02quantumcommunication,

author = {Alexander A. Razborov},

title = {Quantum Communication Complexity of Symmetric Predicates},

journal = {Izvestiya of the Russian Academy of Science, Mathematics},

year = {2002},

volume = {67},

pages = {2003}

}

### Years of Citing Articles

### OpenURL

### Abstract

We completely (that is, up to a logarithmic factor) characterize the bounded-error quantum communication complexity of every predicate f(x; y) (x; y [n]) depending only on jx\yj. Namely, for a predicate D on f0; 1; : : : ; ng let ` 0 (D) = max f` j 1 ` n=2 ^ D(`) 6 D(` 1)g and ` 1 (D) = max fn ` j n=2 ` < n ^ D(`) 6 D(` + 1)g. Then the bounded-error quantum communication complexity of f D (x; y) = D(jx \ yj) is equal (again, up to a logarithmic factor) to ` 1 (D). In particular, the complexity of the set disjointness predicate is n). This result holds both in the model with prior entanglement and without it.