The log of a quantum state and qubit local unitary invariants

Details The log of a quantum state and qubit local unitary invariants The log of a quantum state and qubit local unitary invariants

2010-09-08

arxiv.org/abs/1009.1546v1

Physics

Quantum Physics

14 pages

Scientific paper

Local unitary invariants of multipartite states fall into families related by the tracing-out of subsystems. In the case of pure qubit systems, there is a family that accounts for about half the total number of invariants and is closely connected to multipartite separability. One way to define this family is to give pure states the structure of an algebra, and define a log function in this algebra. The coefficients of the Taylor expansion of this log function, which are polynomials in the coefficients of the states, are cumulants. When twirled by local unitaries, these yield invariants. The traditional cumulant, which is a function of random variables, vanishes if its arguments belong to two or more independent sets. The equivalent of this in our context is that certain cumulant-invariants vanish when a state is separable.

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