A Numerical Evaluation of Entanglement Sharing Protocols Using Quantum LDPC CSS Codes

Masakazu YOSHIDA  Manabu HAGIWARA  Takayuki MIYADERA  Hideki IMAI  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E95-A   No.9   pp.1561-1569
Publication Date: 2012/09/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E95.A.1561
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Information Theory
Keyword: 
entanglement distillation protocol,  quantum error-correcting codes,  quantum low-density parity-check codes,  sum-product decoding,  

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Summary: 
Entangled states play crucial roles in quantum information theory and its applied technologies. In various protocols such as quantum teleportation and quantum key distribution, a good entangled state shared by a pair of distant players is indispensable. In this paper, we numerically examine entanglement sharing protocols using quantum LDPC CSS codes. The sum-product decoding method enables us to detect uncorrectable errors, and thus, two protocols, Detection and Resending (DR) protocol and Non-Detection (ND) protocol are considered. In DR protocol, the players abort the protocol and repeat it if they detect the uncorrectable errors, whereas in ND protocol they do not abort the protocol. We show that DR protocol yields smaller error rate than ND protocol. In addition, it is shown that rather high reliability can be achieved by DR protocol with quantum LDPC CSS codes.