Title :
Mutually Unbiased Bases in 4, 8, and 16 Dimensions Generated by Means of Controlled-Phase Gates With Application to Entangled-Photon QKD Protocols
Author :
Tselniker, Igor ; Nazarathy, Moshe ; Orenstein, Meir
Author_Institution :
Dept. of Electr. Eng., Technion - Israel Inst. of Technol., Haifa, Israel
Abstract :
We design mutually unbiased bases (MUBs) in 4, 8, and 16 dimensions, which are compatible with quadrature phase-shift keying (QPSK) optical transmission, based on novel insights into the structure of the MUB set, viewed as the modulation of a Hadamard matrix with a set of phase masks. The new protocol is based on the generation of a pair of MUBs as tensor products of the lowest dimension (2-D) MUBs, followed by novel unbiasing transformations, which operate on pairs of MUBs and make them mutually unbiased among the pairs. We discovered that the unbiasing transformations consist of controlled-phase quantum gates acting on multiple qubits. We further conceive an abstract BB84-like higher order quantum key distribution MUB-based protocol, based on multiple entangled photons.
Keywords :
Hadamard matrices; cryptographic protocols; quadrature phase shift keying; quantum cryptography; quantum entanglement; quantum gates; quantum optics; Hadamard matrix; controlled-phase quantum gates; entangled-photon QKD protocols; higher order quantum key distribution; multiple entangled photons; multiple qubits; mutually unbiased bases; optical transmission; phase masks; quadrature phase-shift keying; tensor products; unbiasing transformations; Entanglement; Hadamard matrix; integrated optics; mutually unbiased bases (MUBs); optical communication; quadrature phase-shift keying (QPSK); quantum cryptography; quantum key distribution (QKD);
Journal_Title :
Selected Topics in Quantum Electronics, IEEE Journal of
DOI :
10.1109/JSTQE.2009.2021146
