Experimental Solutions to the High-Dimensional Mean King's Problem

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 $72.8\%$, $45.8\%$, 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.

arXiv commentFixed unusual visual aberration in Figure 2, and moved Acknowledgements section

References in corpus (25)

• On mutually unbiased bases
• Quantum teleportation in high dimensions
• On scientific understanding with artificial intelligence
• Automated Search for new Quantum Experiments
• Universal unitary gate for single-photon 2-qubit states
• Experimental investigation of high-dimensional quantum key distribution protocols with twisted photons
• The mean king's problem: Prime degrees of freedom
• Quantum Experiments and Graphs: Multiparty States as coherent superpositions of Perfect Matchings
• Computer-inspired Quantum Experiments
• Pathways for entanglement based quantum communication in the face of high noise
• Quantum Experiments and Graphs II: Quantum Interference, Computation and State Generation
• Conceptual understanding through efficient inverse-design of quantum optical experiments
• Mean king's problem with mutually unbiased bases and orthogonal Latin squares
• Solution to the Mean King's problem with mutually unbiased bases for arbitrary levels
• Ascertaining the Values of ${\sigma }_x$, ${\sigma }_y$, and ${\sigma }_z$ of a Polarization Qubit
• Secure key distribution via pre- and post-selected quantum states
• Quantum cryptography as a retrodiction problem
• A Meaner King uses Biased Bases
• Solution to the mean king's problem using quantum error-correcting codes
• Experimental Test of Tracking the King Problem
• Experimental Solutions to the High-Dimensional Mean King's Problem
• The intercept/resend and translucent attacks on the quantum key distribution protocol based on the pre- and post-selection effect
• The "mean king's problem" with continuous variables
• Geometrical view of the Mean King Problem
• A 2-Categorical Analysis of Complementary Families, Quantum Key Distribution and the Mean King Problem

Cited by in corpus (3)

• Experimental Solutions to the High-Dimensional Mean King's Problem
• Retrodiction of measurement outcomes on a single quantum system reveals entanglement with its environment
• Deep Quantum Graph Dreaming: Deciphering Neural Network Insights into Quantum Experiments