July, 2023. arXiv:2307.12938 [quant-ph]

Paper doi abstract bibtex

Paper doi abstract bibtex

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.

@misc{jaouni_experimental_2023, title = {Experimental {Solutions} to the {High}-{Dimensional} {Mean} {King}'s {Problem}}, url = {http://arxiv.org/abs/2307.12938}, doi = {10.48550/arXiv.2307.12938}, abstract = {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 {\textbackslash}\%\$, \$45.8{\textbackslash}\%\$, and \$34.8 {\textbackslash}\%\$, 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.}, urldate = {2023-07-29}, publisher = {arXiv}, author = {Jaouni, Tareq and Gao, Xiaoqin and Arlt, Sören and Krenn, Mario and Karimi, Ebrahim}, month = jul, year = {2023}, note = {arXiv:2307.12938 [quant-ph]}, keywords = {mentions sympy, quantum entanglement, quantum physics}, }

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