We present a mathematical proof of the algorithm allowing one to generate all---symmetric and nonsymmetric---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.
We propose a scheme enabling the universal coupling of angular momentum of
N remote noninteracting qubits using linear optical tools only. Our system consists of
N single-photon emitters in a $\ensuremath{\Lambda}$ configuration that are entangled among their long-lived ground-state qubits through suitably designed measurements of the emitted photons. In this manner, we present an experimentally feasible algorithm that is able to generate any of the
2N symmetric and nonsymmetric total angular momentum eigenstates spanning the Hilbert space of the
N-qubit compound.
We propose a method for the generation of a large variety of entangled states, encoded in the polarization degrees of freedom of
N photons, within the same experimental setup. Starting with uncorrelated photons, emitted from
N arbitrary single-photon sources, and using linear optical tools only, we demonstrate the creation of all symmetric states (e.g., GHZ and
W states), as well as all symmetric and nonsymmetric total angular momentum eigenstates of the
N-qubit compound.