Quantum divisibility test and its application in mesoscopic physics

TL;DR

This paper introduces a quantum algorithm that converts the number of particles in a quantum wire into a binary number, enabling applications like divisibility testing and entanglement generation in mesoscopic physics.

Contribution

It presents a novel quantum algorithm for counting particles and applying it to divisibility tests and entanglement schemes in mesoscopic systems.

Findings

Efficient quantum counting of particles using log2 N qubits.

One-shot measurement for particle number divisibility.

Scheme for generating entangled multi-particle states.

Abstract

We present a quantum algorithm to transform the cardinality of a set of charged particles flowing along a quantum wire into a binary number. The setup performing this task (for at most N particles) involves log_2 N quantum bits serving as counters and a sequential read out. Applications include a divisibility check to experimentally test the size of a finite train of particles in a quantum wire with a one-shot measurement and a scheme allowing to entangle multi-particle wave functions and generating Bell states, Greenberger-Horne-Zeilinger states, or Dicke states in a Mach-Zehnder interferometer.