Properties of Product Operators

We have seen that several density matrices can be expressed in terms of products and sums of spin operators. It can be shown that for a system of N spin /2 nuclei any density matrix can be formualted as a linear combination of 4N spin 

Transverse magnetization (single quantum coherence) Transverse / magnetization, antiphase in S Transverse S magnetization, antiphase in / 

Identity operator (unit matrix), needed for completeness 

For larger spin systems, a number of three-spin product operators may appear, for example  

4IXSZTZ Ix magnetization in antiphase with respect to 5 and T 4IXSXTZ Two-spin coherence in antiphase with respect to T, the passive spin 4IXSXTX Three-spin coherence 

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