Zero-error source-channel coding with entanglement

Seminar date and time: 
Tuesday, 9 April, 2013 - 11:30
Affiliation: 
CWI, Amsterdam
Author: 
Giannicola Scarpa
Location: 
IFAE seminar room (UAB)

We study the use of entanglement in the zero-error source-channel coding problem.
Here, Alice and Bob are connected by a noisy classical one-way channel, and are given correlated inputs from a random source. Their goal is for Bob to learn Alice's input while using the channel as little as possible. It was recently shown that entanglement allows for a separation between the Shannon capacity of a graph and its entanglement-assisted variant.
Here we show that entanglement can allow for an unbounded decrease in the asymptotic rate of classical source-channel codes. Our proof uses low-degree polynomials due to Barrington, Beigel and Rudich, Hadamard matrices due to Xia and Liu and a novel application of the quantum teleportation scheme of Bennett et al. We also prove a lower bound on the rate of entanglement-assisted source-codes in terms of a variant of the Lov asz theta number introduced by Szegedy, a graph parameter given by a semidefinite program.

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