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Single Qubit Private Quantum Channels and 3-Dimensional Regular Polyhedra
New Phys.: Sae Mulli
Published online December 18, 2017;  
© 2017 New Physics: Sae Mulli.

Kabgyun Jeong*, Jun Seo Lee, Jin Tae Choi, Seok Min Hong, Myung Gu Jung, Gyeong Beom Kim, Jae Kwon Kim, Suntaek Kim**
Received November 1, 2017; Revised November 23, 2017; Accepted December 18, 2017.
Private quantum channel (PQC) in quantum cryptography is one of the most well-known quantum cryptographic protocols using a secret key obtained from quantum key distribution (QKD) protocol, and it is called as quantum one-time pad or random unitary channel and so on. The reason why PQC is important is that the output state of the channel always gives rise to maximally mixed state, so it is possible to secure quantum communication without any external eavesdropping; thus it preserves information-theoretic security. We explicitly construct five kinds of a single qubit PQC and try to connect those to 3-dimensional polyhedra respectively. 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 matrices are naturally connected to a pre-shared key obtained by QKD protocol, it completes a model of five kinds of PQC for the single qubit state. Finally, we analyze a trade-off relation between security and efficiency for the PQC.

January 2018, 68 (1)
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