Local unitary versus local Clifford equivalence of stabilizer states

We study the relation between local unitary (LU) equivalence and local Clifford (LC) equivalence of stabilizer states. We introduce a large subclass of stabilizer states, such that every two LU equivalent states in this class are necessarily LC equivalent. Together with earlier results, this shows that LC, LU and SLOCC equivalence are the same notions for this class of stabilizer states. Moreover, recognizing whether two given stabilizer states in the present subclass are locally equivalent only requires a polynomial number of operations in the number of qubits.Comment: 8 pages, replaced with published versio

Edge local complementation for logical cluster states

A method is presented for the implementation of edge local complementation in graph states, based on the application of two Hadamard operations and a single controlled-phase (CZ) gate. As an application, we demonstrate an efficient scheme to construct a one-dimensional logical cluster state based on the five-qubit quantum error-correcting code, using a sequence of edge local complementations. A single physical CZ operation, together with local operations, is sufficient to create a logical CZ operation between two logical qubits. The same construction can be used to generate any encoded graph state. This approach in concatenation may allow one to create a hierarchical quantum network for quantum information tasks.Comment: 15 pages, two figures, IOP styl

Entanglement on mixed stabilizer states: normal forms and reduction procedures

Published versio