**Mathematical characterization of entanglement:
**higher dimensional composite systems – from qubits to qudits, entanglement measures, entanglement witnesses and geometry of quantum states, relativistic effects in quantum entanglement, noninertial frames, Unruh effect, gravitation and black holes

**Relativistic entanglement:
**Entanglement of two propagating particles with spin, Alice & Bob, considered as a 4 qubit system and observed by the relativistically boosted observer Eve.

For reference, see N. Friis, R. A. Bertlmann, M. Huber and B. C. Hiesmayr, Phys. Rev. A81, 042114 (2010); arXiv: 0912.4863 [quant-ph].

**Alice cannot communicate anymore with Bob:**

Alice and Bob share a maximal entangled state of two fermions. Alice, when falling into a black hole, although remaining entangled with Bob, cannot communicate on a quantum information level with Bob who is resting near the horizon. Thus quantum mechanics cannot overcome relativity !

For reference, see “Residual entanglement of accelerated fermions is not nonlocal”, N. Friis, P. Köhler, M. Martin-Martinez, and R.A. Bertlmann, Phys. Rev. A84, 062111 (2011), and arXiv:1107.3235 [quant-ph].