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arXiv · 2007.01007

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

Armin Tavakoli·Ingemar Bengtsson·Nicolas Gisin·Joseph M. Renes
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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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Armin Tavakoli, Ingemar Bengtsson, Nicolas Gisin, Joseph M. Renes. 2020-07-02. Compounds of symmetric informationally complete measurements and their application in quantum key distribution. https://doi.org/10.1103/physrevresearch.2.043122

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