NMR Investigation of the Quantum Piegonhole Effect

TL;DR

This paper uses a four-qubit NMR quantum simulator to experimentally investigate the quantum pigeon-hole effect, demonstrating scenarios where three particles appear to occupy only two containers without sharing, in line with quantum predictions.

Contribution

First experimental demonstration of the quantum pigeon-hole effect using a four-qubit NMR quantum simulator, confirming theoretical predictions.

Findings

Experimental results agree with quantum theory

Quantum pigeon-hole effect observed in NMR system

Noninvasive joint probing of qubit states achieved

Abstract

Quantum simulators based on nuclear spin-systems controlled by NMR techniques have been used for studying various quantum phenomena. In this work, using a four-qubit NMR quantum simulator, we investigate the recently postulated quantum pigeon-hole effect. In mathematics, the pigeonhole effect is described by a set of three objects being allocated with only two containers. Classically, one would expect at least one container to accommodate more than one object. However, recently it was predicted that there exist quantum scenarios wherein three quantum particles appear to reside in two containers in such a way that no two particles can be simultaneously assigned with a single container. In our experiments, quantum pigeons are emulated by three nuclear qubits whose states are probed jointly and noninvasively by an ancillary spin. The qubit-states $\{\ket{0}$, $\ket{1}\}$ emulate the two containers available for each of the qubits. The experimental results are in good agreement with quantum theoretical predictions.