Simulating the coupling of angular momenta in distant matter qubits

TL;DR

This paper proves that an existing algorithm can generate all total angular momentum eigenstates in remote matter qubits, effectively simulating angular momentum coupling without direct particle interaction.

Contribution

It provides a mathematical proof and recursion formula confirming the algorithm's ability to simulate angular momentum coupling in remote matter qubits.

Findings

The algorithm generates states equivalent to quantum angular momentum eigenstates.

It can simulate coupling of N spin-1/2 systems remotely.

The method implements Clebsch-Gordan coefficients without direct interaction.

Abstract

We present a mathematical proof of the algorithm allowing to generate all - symmetric and non-symmetric - total angular momentum eigenstates in remote matter qubits by projective measurements, proposed in Maser et al. [Phys. Rev. A 79, 033833 (2009)]. By deriving a recursion formula for the algorithm we show that the generated states are equal to the total angular momentum eigenstates obtained via the usual quantum mechanical coupling of angular momenta. In this way we demonstrate that the algorithm is able to simulate the coupling of N spin-1/2 systems, and to implement the required Clebsch-Gordan coefficients, even though the particles never directly interact with each other.