Optimal QRAC strategies and an extension of the MUB condition

2017. 04. 19. 10:00
Farkas Máté (Gdansk)

Quantum random access codes (QRACs) have been studied by many groups in the quantum information community, and found applications in the context of quantum finite automata, quantum communication complexity, and recently (by our group in Gdansk) in dimension witnesses beyond non-classicality tests. It is a simple prepare-and-measure protocol, which I will briefly introduce. Then, I will focus on our recent results on optimal QRAC strategies. It is shown, that in a simple case, optimal measurements are given by mutually unbiased bases (MUBs). Apart from this task, MUBs are of great interest in the community, being extremely useful in quantum state tomography, quantum state disrcimination and quantum key distribution. It turns out that for general QRACs, the MUB condition is not sufficient to give optimal measurements. Optimization over possible quantum strategies leads to a generalization of the MUB condition to a global condition on more than two (n) bases, which I call the nUB condition (n-fold unbiased bases). At this point it is unclear if these bases can be constructed within the framework of quantum mechanics, although probabilistic arguments support their existence in high dimensions, and 3UBs trivially appear in dimension 2. Nevertheless, they give close-to-tight upper bounds on the average success probability of QRACs in general cases, and have the potential of applications in other tasks normally related to MUBs (such as quantum key distribution or entropic uncertainty relations). In the talk I will present the nUB conditions and their natural appearance in the QRAC scenario, and discuss their properties and potential applications.