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

Masakazu YOSHIDA, Manabu HAGIWARA, Takayuki MIYADERA, Hideki IMAI

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Masakazu YOSHIDA
Graduate School of Science and Engineering, Chuo University
Manabu HAGIWARA
Research Center for Information Security (RCIS), National Institute of Advanced Industrial Science and Technology (AIST)
Research and Development Initiative, Chuo University
Takayuki MIYADERA
Research Center for Information Security (RCIS), National Institute of Advanced Industrial Science and Technology (AIST)
Research and Development Initiative, Chuo University
Hideki IMAI
Graduate School of Science and Engineering, Chuo University

Corresponding author

Keywords:entanglement distillation protocol,quantum error-correcting codes,quantum low-density parity-check codes,sum-product decoding

JOURNALRESTRICTED ACCESS

2012 Volume E95.AIssue 9Pages 1561-1569

DOIhttps://doi.org/10.1587/transfun.E95.A.1561

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Published: September 01, 2012Manuscript Received: November 18, 2011Released on J-STAGE: September 01, 2012Accepted: -Advance online publication: -Manuscript Revised: April 28, 2012

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Abstract

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.

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