Papers › Experimental Solutions to the High-Dimensional Mean King's Problem
Experimental Solutions to the High-Dimensional Mean King's Problem
Tareq Jaouni, Xiaoqin Gao, Sören Arlt, Mario Krenn, Ebrahim Karimi
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In 1987, Vaidman, Aharanov, and Albert put forward a puzzle called the Mean King's Problem (MKP) that can be solved only by harnessing quantum entanglement. Prime-powered solutions to the problem have been shown to exist, but they have not yet been experimentally realized for any dimension beyond two. We propose a general first-of-its-kind experimental scheme for solving the MKP in prime dimensions (D). Our search is guided by the digital discovery framework PyTheus, which finds highly interpretable graph-based representations of quantum optical experimental setups; using it, we find specific solutions and generalize to higher dimensions through human insight. As proof of principle, we present a detailed investigation of our solution for the three-, five-, and seven-dimensional cases. We obtain maximum success probabilities of 72.8 %, 45.8%, and 34.8 %, respectively. We, therefore, posit that our computer-inspired scheme yields solutions that exceed the classical probability (1/D) twofold, demonstrating its promise for experimental implementation.
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