Communication cost of classically simulating a quantum channel with subsequent rank-1 projective measurement
Abstract
A process of preparation, transmission and subsequent projective measurement of a qubit can be simulated by a classical model with only two bits of communication and some amount of shared randomness. However no model for n qubits with a finite amount of classical communication is known at present. A lower bound for the communication cost can provide useful hints for a generalization. It is known for example that the amount of communication must be greater than c 2^n, where c~0.01. The proof uses a quite elaborate theorem of communication complexity. Using a mathematical conjecture known as the "double cap conjecture", we strengthen this result by presenting a geometrical and extremely simple derivation of the lower bound 2^n-1. Only rank-1 projective measurements are involved in the derivation.
Keywords
Cite
@article{arxiv.1110.5944,
title = {Communication cost of classically simulating a quantum channel with subsequent rank-1 projective measurement},
author = {Alberto Montina},
journal= {arXiv preprint arXiv:1110.5944},
year = {2011}
}
Comments
corrected some minor typos