Quantum Entanglement and Algebraic Group Actions

Robert Furber

Published Jan 1, 2011• 0 citations

Abstract

In the following we discuss how algebraic group actions can be applied to the study of quantum entanglement. The following facts are new: • A method for calculating equations for the SLOCC class of any pure state, with no restrictions on dimensions other than those imposed by computational speed. • A calculation of the equations defining the closure of one 4-partite state, as an example to illustrate the method. • To my knowledge, it has not previously been observed that SLOCC classes equal if their closure is equal, although the fact about algebraic group actions is known. • Similarly, the fact that a SLOCC class inside the closure of another must be of strictly smaller dimension. We also discuss quotients of the space of states by the action, but do not actually compute any or prove new theorems in this area.

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