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
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].