# Likelihood Theory in a Quantum World: tests with Quantum coins and computers

## TL;DR

This paper explores improved methods for determining the fairness of quantum coins using entangled measurements on qubits, demonstrating enhanced confidence over classical approaches through simulations on IBM quantum computers.

## Contribution

It introduces a novel entanglement-based measurement strategy that increases confidence in quantum coin fairness testing compared to traditional methods.

## Key findings

- Entanglement improves confidence in quantum coin tests
- Simulation results confirm the effectiveness of the proposed strategy
- Quantum measurement strategies outperform classical ones in this context

## Abstract

By repeated trials, one can determine the fairness of a classical coin with a confidence which grows with the number of trials. A quantum coin can be in a superposition of heads and tails and its state is most generally a density matrix. Given a string of qubits representing a series of trials, one can measure them individually and determine the state with a certain confidence. We show that there is an improved strategy which measures the qubits after entangling them, which leads to a greater confidence. This strategy is demonstrated on the simulation facility of IBM quantum computers.