# Experimental Test of Tracking the King Problem

## TL;DR

This paper reports the first experimental test of a variant of the Mean King Problem, demonstrating quantum retrodiction using entanglement and controlled-not gates, revealing new insights into quantum measurement and communication.

## Contribution

It provides the first experimental validation of the 'Tracking the King' problem, showcasing quantum retrodiction without measurement outcome knowledge.

## Key findings

- Successful retrodiction of the King's measurement choice.
- Quantum communication of hidden measurement information.
- Validation of entanglement-based retrodiction methods.

## Abstract

In quantum theory, the retrodiction problem is not as clear as its classical counterpart because of the uncertainty principle of quantum mechanics. In classical physics, the measurement outcomes of the present state can be used directly for predicting the future events and inferring the past events which is known as retrodiction. However, as a probabilistic theory, quantum-mechanical retrodiction is a nontrivial problem that has been investigated for a long time, of which the Mean King Problem is one of the most extensively studied issues. Here, we present the first experimental test of a variant of the Mean King Problem, which has a more stringent regulation and is termed "Tracking the King". We demonstrate that Alice, by harnessing the shared entanglement and controlled-not gate, can successfully retrodict the choice of King's measurement without knowing any measurement outcome. Our results also provide a counterintuitive quantum communication to deliver information hidden in the choice of measurement.