Entanglement-Assisted Zero-Error Source-Channel Coding

We study the use of quantum 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...

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Vydáno v:IEEE transactions on information theory Ročník 61; číslo 2; s. 1124 - 1138
Hlavní autoři: Briët, Jop, Buhrman, Harry, Laurent, Monique, Piovesan, Teresa, Scarpa, Giannicola
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York IEEE 01.02.2015
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:
Channel coding
Correlation analysis
Entanglement
Error correction & detection
graph coloring
graph homomorphism
Lov´asz theta number
Mathematical problems
Numerical analysis
Polynomials
Protocols
Quantum entanglement
Quantum physics
quantum remote state preparation
Random variables
Registers
Shannon capacity
Source coding
Witsenhausen rate
semidefinite programming
graph homomorphism
Witsenhausen rate
Lovász theta number
Entanglement
graph coloring
Shannon capacity
quantum remote state preparation
ISSN:0018-9448, 1557-9654
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Popis
Shrnutí:We study the use of quantum 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. In the zero-error regime, the optimal rates of source codes and channel codes are given by graph parameters known as the Witsenhausen rate and Shannon capacity, respectively. The Lovász theta number, a graph parameter defined by a semidefinite program, gives the best efficiently computable upper bound on the Shannon capacity and it also upper bounds its entanglement-assisted counterpart. At the same time, it was recently shown that the Shannon capacity can be increased if Alice and Bob may use entanglement. Here, we partially extend these results to the source-coding problem and to the more general source-channel coding problem. We prove a lower bound on the rate of entanglement-assisted source-codes in terms of Szegedy's number (a strengthening of the theta number). This result implies that the theta number lower bounds the entangled variant of the Witsenhausen rate. We also show that entanglement can allow for an unbounded improvement of the asymptotic rate of both classical source codes and classical source-channel codes. Our separation results use low-degree polynomials due to Barrington, Beigel and Rudich, Hadamard matrices due to Xia and Liu, and a new application of remote state preparation.
Bibliografie:SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2014.2385080