Non-Local Parity Measurements and the Quantum Pigeonhole Effect

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.

5 pages, 2 figures

References in corpus (4)

• Interaction-free measurements with superconducting qubits
• Generalized partial measurements
• A quantum no-reflection theorem and the speeding up of Grover's search algorithm
• Realism and single-quanta nonlocality

Cited by in corpus (4)

• Quantum simulation of parity-time symmetry breaking with a superconducting quantum processor
• Photonic realization of erasure-based nonlocal measurements
• $\mathcal{P}\mathcal{T}$-symmetric mapping of three states and its implementation on a cloud quantum processor
• Quantum process tomography of adiabatic and superadiabatic stimulated Raman passage