Communication complexity of remote state preparation with entanglement

We consider the problem of remote state preparation recently studied in several papers. We study the communication complexity of this problem, in the presence of entanglement and in the scenario of single use of the channel.Comment: 4 pages, no figure, ver3: Version to appear in Quantum information and computatio

A Parallel Approximation Algorithm for Positive Semidefinite Programming

Positive semidefinite programs are an important subclass of semidefinite programs in which all matrices involved in the specification of the problem are positive semidefinite and all scalars involved are non-negative. We present a parallel algorithm, which given an instance of a positive semidefinite program of size N and an approximation factor eps > 0, runs in (parallel) time poly(1/eps) \cdot polylog(N), using poly(N) processors, and outputs a value which is within multiplicative factor of (1 + eps) to the optimal. Our result generalizes analogous result of Luby and Nisan [1993] for positive linear programs and our algorithm is inspired by their algorithm.Comment: 16 page