Experimental Solutions to the High-Dimensional Mean King's Problem
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866909101120815104 |
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| author | Jaouni, Tareq Gao, Xiaoqin Arlt, Sören Krenn, Mario Karimi, Ebrahim |
| author_facet | Jaouni, Tareq Gao, Xiaoqin Arlt, Sören Krenn, Mario Karimi, Ebrahim |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_12938 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Experimental Solutions to the High-Dimensional Mean King's Problem Jaouni, Tareq Gao, Xiaoqin Arlt, Sören Krenn, Mario Karimi, Ebrahim Quantum Physics 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. |
| title | Experimental Solutions to the High-Dimensional Mean King's Problem |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2307.12938 |