# Non-Local Parity Measurements and the Quantum Pigeonhole Effect

## TL;DR

This paper demonstrates that quantum correlations can violate the classical pigeonhole principle through non-local measurements, using explicit constructions with standard quantum gates and measurements, highlighting the non-local nature of quantum entanglement.

## Contribution

It provides explicit non-local quantum measurement procedures that violate the pigeonhole principle, emphasizing the role of non-local correlations in quantum physics.

## Key findings

- Quantum pigeonhole principle can be violated with non-local measurements.
- Explicit constructions use standard quantum gates and measurements.
- Violations occur without direct interactions between particles.

## Abstract

The pigeonhole principle upholds the idea that by ascribing to three different particles either one of two properties, we necessarily end up in a situation when at least two of the particles have the same property. In quantum physics, this principle is violated in experiments involving postselection of the particles in appropriately-chosen states. Here, we give two explicit constructions using standard gates and measurements that illustrate this fact. Intriguingly, the procedures described are manifestly non-local, which demonstrates that the correlations needed to observe the violation of this principle can be created without direct interactions between particles.