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arXiv:2307.12938 · Optica Quantum

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

Tareq Jaouni, Xiaoqin Gao, Sören Arlt, Mario Krenn, Ebrahim Karimi

Published Nov 17, 2023• 3 citations
arXivHTMLPDF

Abstract

Vaidman, Aharanov, and Albert [ Phys. Rev. Lett. 58 ( 14 ), 1385 ( 1987 ) 10.1103/PhysRevLett.58.1385 ] 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%, 56.2%, and 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.

DOI
10.1364/opticaq.502451

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Vaidman, Aharanov, and Albert [ Phys. Rev. Lett. 58 ( 14 ), 1385 ( 1987 ) 10.1103/PhysRevLett.58.1385 ] 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%, 56.2%, and 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.
Photons are the physical system of choice for performing experimental tests of the foundations of quantum mechanics. Furthermore, photonic quantum technology is a main player in the second quantum revolution, promising the development of better sensors, secure communications, and quantum-enhanced computation. These endeavors require generating specific quantum states or efficiently performing quantum tasks. The design of the corresponding optical experiments was historically powered by human creativity but is recently being automated with advanced computer algorithms and artificial intelligence. While several computer-designed experiments have been experimentally realized, this approach has not yet been widely adopted by the broader photonic quantum optics community. The main roadblocks consist of most systems being closed-source, inefficient, or targeted to very specific use-cases that are difficult to generalize. Here, we overcome these problems with a highly-efficient, open-source digital discovery framework PyTheus, which can employ a wide range of experimental devices from modern quantum labs to solve various tasks. This includes the discovery of highly entangled quantum states, quantum measurement schemes, quantum communication protocols, multi-particle quantum gates, as well as the optimization of continuous and discrete properties of quantum experiments or quantum states. PyTheus produces interpretable designs for complex experimental problems which human researchers can often readily conceptualize. PyTheus is an example of a powerful framework that can lead to scientific discoveries – one of the core goals of artificial intelligence in science. We hope it will help accelerate the development of quantum optics and provide new ideas in quantum hardware and technology.
Photonic technologies are main players in the second quantum revolution, providing better sensors, secure communications, and quantum-enhanced computation. Such endeavors require generating specific quantum states or efficiently performing quantum tasks. The design of the corresponding optical experiments, historically powered by human creativity, is being slowly automated by novel algorithms. Unfortunately, these tools are often restricted to very specific use cases and are difficult to generalize, which limits their practical implementation. To overcome these challenges, we developed PyTheus, a highly efficient, open-source digital discovery framework based on a graph-based representation of optical setups, which includes a wide range of modern experimental devices. PyTheus produces interpretable designs to solve complex experimental problems, like entanglement generation and distribution. Aiming for the simplest solutions, our software provides deeper understanding to human researchers, which can generalize the findings. Therefore, PyTheus can accelerate the development of quantum optics and related technologies.
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Quantum entanglement plays an important role in quantum information processes, such as quantum computation and quantum communication. Experiments in laboratories are unquestionably crucial to increase our understanding of quantum systems and inspire new insights into future applications. However, there are no general recipes for the creation of arbitrary quantum states with many particles entangled in high dimensions. Here we exploit a recent connection between quantum experiments and graph theory and answer this question for a plethora of classes of entangled states. We find experimental setups for Greenberger-Horne-Zeilinger states, WWW states, general Dicke states, and asymmetrically high-dimensional multipartite entangled states. This result sheds light on the producibility of arbitrary quantum states using photonic technology with probabilistic pair sources and allows us to understand the underlying technological and fundamental properties of entanglement.
Finite geometry is used to underpin finite, d2d^2d2, dimensional Hilbert space accommodating two particles, d dimensional each. d=prime ≠2\ne2=2. Central role is allotted to states with mutual unbiased bases (MUB) labelling underpinned with points of finite dual affine plane geometry (DAPG). The DAPG lines are shown to underpin maximally entangled states which form an orthonormal basis spanning the space and provide a novel, geometrical view to a new solution of the Mean King Problem (MKP). Brief expositions to the topics considered: MUB, DAPG and the MKP are included rendering the paper self contained.