For quantum systems with two or more interacting subsystems the subsystems become entangled such that each is no longer in a pure quantum state. For systems with only two subsystems this entanglement can be described by using the Schmidt decomposition which selects a preferred orthonormal basis for expressing the wave function and gives a measure of the degree of entanglement present in the system. However, a solution for the more general case of n subsystems is not yet known. We present here a review of this process using the standard representation and apply this method to the geometric algebra representation which has the advantage of more easily generalising to n subsystems.

c.doran@mrao.cam.ac.uk