Experimental solutions to the high-dimensional mean king’s problem

Abstract

Vaidman, Aharanov, and Albert [Phys. Rev. Lett. 58(14), 1385 (1987) [CrossRef] ] 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 82.3%$82.3{\% }$, 56.2%$56.2{\% }$, and 35.5%$35.5 {\% }$, respectively. We therefore posit that our computer-inspired scheme yields solutions that implement Alice’s strategy with quantum advantage, demonstrating its promise for experimental implementation in quantum communication tasks.