We derive a family of necessary separability criteria for finite-dimensional systems based on inequalities for variances of observables. We show that every pure bipartite entangled state violates some of these inequalities. Furthermore, a family of bound entangled states and true multipartite entangled states can be detected. The inequalities also allow us to distinguish between different classes of true tripartite entanglement for qubits. We formulate an equivalent criterion in terms of covariance matrices. This allows us to apply criteria known from the regime of continuous variables to finite-dimensional systems.
Physical Review Letters
- Pub Date:
- March 2004
- Entanglement production characterization and manipulation;
- Entanglement and quantum nonlocality;
- Quantum Physics
- 4 pages, no figures. v2: Some discussion added, main results unchanged