(1 -Δ𝑝)1 -+ Δ𝑝𝜌 > 678, where 𝜌 > 678, is the pure state. Measurements performed on a single-spin system with a pseudo-pure initial state are functionally identical to those performed with a truly pure initial state, with the only difference being a reduction in signal intensity. The same is not true for a two-spin system, where the expectation value of 2𝑆 0 ' 𝐼 0 ' in 𝜌 > 678, depends on Δ𝑝. For clarity the identity element will be omitted from further discussion, as it is invariant under unitary transformations and is not measurable. As such all subsequently defined density matrices represent traceless deviation density matrices, as is common in magnetic resonance. We note, however, that for a two-MESQ system at achievable temperatures and magnetic fields, the amplitude of 𝜌 > 678, can exceed the threshold required to demonstrate real entanglement rather than pseudo-entanglement. In principle entanglement between two coupled spins could be generated by driving the |00⟩ ↔ |11⟩ and |10⟩ ↔ |01⟩ conditional transitions with resonant pulses. This will be most convenient in the intermediate coupling regime (𝜔 )* ≈ |𝜔 ) -𝜔 * |) in which case all possible transitions are spectrally addressable and have similar EPR transition matrix elements. In weakly coupled systems for which the coupling is too small to yield spectrally-addressable conditional transitions, it is more convenient to generate entanglement by allowing the system to freely evolve under its coupling Hamiltonian. This method is easier to implement as it is only necessary to pulse at two frequencies (resonant with S and I) and was first demonstrated in NMR using a Dual-Frequency Hahn-Echo sequence (Figure , right). In a Single-Frequency Hahn Echo (SFHE) sequence (Figure , left), coherences are generated on spin S at time 0 0 , and are completely refocussed into an echo at time 2𝜏. The magnetisation of the I spin is unaffected by the pulses and as such the density matrix when the echo is formed (assuming pulses are applied along +𝑥) is given by: