We introduce a physically motivated classification of pure quantum states describing $n$ qubits. We characterize all multipartite states which can be maximally entangled to local auxiliary systems using controlled operations. A state has this property if and only if one can construct out of it an orthonormal basis by applying independent local unitary operations. This implies that those states can be used to encode locally the maximum amount of $n$ independent bits. Examples of these states are the so-called stabilizer states, which are used for quantum error correction and one-way quantum computing. We give a simple characterization of these states and construct a complete set of commuting unitary observables which characterize the state uniquely. Furthermore we show how these states can be prepared and discuss their applications.

• Received 22 September 2008

DOI:https://doi.org/10.1103/PhysRevA.79.052304