Quantum Lorentz-group invariants ofn-qubit systems

Abstract

We consider the behavior of quantum states under stochastic local quantum operations and classical communication (SLOCC) for an arbitrary fixed number of qubits. We use a real (Lorentz) group to describe the action of SLOCC operations on n-qubit states. We discuss the natural quantum Lorentz-group group-invariant length for an arbitrary number of qubits. We relate this approach to that based on local operations and classical communication and provide an example of how the invariant length can be used to describe entanglement. We also note that this invariant length is the Minkowskian analog to the quantum state purity, which is the corresponding Euclidean length.