20 research outputs found
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
Short proofs of the Quantum Substate Theorem
The Quantum Substate Theorem due to Jain, Radhakrishnan, and Sen (2002) gives
us a powerful operational interpretation of relative entropy, in fact, of the
observational divergence of two quantum states, a quantity that is related to
their relative entropy. Informally, the theorem states that if the
observational divergence between two quantum states rho, sigma is small, then
there is a quantum state rho' close to rho in trace distance, such that rho'
when scaled down by a small factor becomes a substate of sigma. We present new
proofs of this theorem. The resulting statement is optimal up to a constant
factor in its dependence on observational divergence. In addition, the proofs
are both conceptually simpler and significantly shorter than the earlier proof.Comment: 11 pages. Rewritten; included new references; presented the results
in terms of smooth relative min-entropy; stronger results; included converse
and proof using SDP dualit