Computing Local Invariants of Qubit Systems

Details Computing Local Invariants of Qubit Systems Computing Local Invariants of Qubit Systems

1997-12-18

arxiv.org/abs/quant-ph/9712040v2

Phys.Rev.A58:1833-1839,1998

Physics

Quantum Physics

8 pages, RevTeX, submitted to PRA; example added to demonstrate the application of the invariants

Scientific paper

10.1103/PhysRevA.58.1833

We investigate means to describe the non-local properties of quantum systems and to test if two quantum systems are locally equivalent. For this we consider quantum systems that consist of several subsystems, especially multiple qubits. We compute invariant polynomials, i. e., polynomial functions of the entries of the density operator which are invariant under local unitary operations. As an example, we consider a system of two qubits. We compute the Molien series for the corresponding representation which gives information about the number of linearly independent invariants. Furthermore, we present a set of polynomials which generate all invariants (at least) up to degree 23. Finally, the use of invariants to check whether two density operators are locally equivalent is demonstrated.

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