Compounds of symmetric informationally complete measurements and their application in quantum key distribution

• URL: http://arxiv.org/abs/2007.01007v1
• Date: Thu, 2 Jul 2020 10:43:21 GMT
• Title: Compounds of symmetric informationally complete measurements and their application in quantum key distribution
• Authors: Armin Tavakoli, Ingemar Bengtsson, Nicolas Gisin and Joseph M. Renes
• Abstract summary: We introduce a more sophisticated discrete structure compounded by several SICs. A SIC-compound is defined to be a collection of $d3$ vectors in $d$-dimensional Hilbert space. We show that SIC-compounds enable secure key generation in the presence of errors that are large enough to prevent the success of the generalisation of the six-state protocol.
• Score: 6.117371161379207
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Symmetric informationally complete measurements (SICs) are elegant, celebrated and broadly useful discrete structures in Hilbert space. We introduce a more sophisticated discrete structure compounded by several SICs. A SIC-compound is defined to be a collection of $d^3$ vectors in $d$-dimensional Hilbert space that can be partitioned in two different ways: into $d$ SICs and into $d^2$ orthonormal bases. While a priori their existence may appear unlikely when $d>2$, we surprisingly answer it in the positive through an explicit construction for $d=4$. Remarkably this SIC-compound admits a close relation to mutually unbiased bases, as is revealed through quantum state discrimination. Going beyond fundamental considerations, we leverage these exotic properties to construct a protocol for quantum key distribution and analyze its security under general eavesdropping attacks. We show that SIC-compounds enable secure key generation in the presence of errors that are large enough to prevent the success of the generalisation of the six-state protocol.

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