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Single Qubit Private Quantum Channels and 3-Dimensional Regular Polyhedra
New Phys.: Sae Mulli 2018; 68: 232~240
Published online February 28, 2018;
© 2018 New Physics: Sae Mulli.

Kabgyun JEONG*1, Jun Seo LEE2, Jin Tae CHOI2, Seok Min HONG2, Myung Gu JUNG2, Gyeong Beom KIM2, Jae Kwon KIM2, Suntaek KIM†2

1 Department of Physics and Astronomy, Seoul National University, Seoul 08826, Korea
2 Chungnam Science High School, Kongju 32620, Korea
Correspondence to: *, †
Received November 1, 2017; Revised November 23, 2017; Accepted December 18, 2017.
cc This is an open-access article distributed under the terms of the Creative Commons Attribution Non-Commercial License ( which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
A private quantum channel (PQC) in quantum cryptography is one of the most well-known quantum cryptographic protocols using a secret key obtained from the quantum key distribution (QKD) protocol, and it is called a quantum one-time pad or random unitary channel and so on. The reason a PQC is important is that the output state of the channel always gives rise to a maximally mixed state, so the quantum communication can be secured without any external eavesdropping; thus, it preserves information-theoretic security. We explicitly construct five kinds of single-qubit PQCs and try to connect each to a 3-dimensional polyhedron. We expand a corresponding method between four unitary matrices given by Pauli matrices and the regular tetrahedron, and find specific unitary matrices corresponding to another four regular polyhedra. Each unitary matrix is naturally connected to a pre-shared key obtained by using the QKD protocol, which completes a model of five kinds of PQCs for the single-qubit state. Finally, we analyze a trade-off relation between security and efficiency for the PQC.
PACS numbers: 03.67.-a, 03.67.Dd, 03.67.Hk
Keywords: Quantum cryptography, Quantum key distribution protocol, Private quantum channel, Maximally mixed state, Regular polyhedron

July 2018, 68 (7)
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