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Zbl 1065.81521
Caban, P.; Podlaski, K.; Rembieliński, J.; Smoliński, K.A.; Walczak, Z.
Entanglement and tensor product decomposition for two fermions. (English)
[J] J. Phys. A, Math. Gen. 38, No. 6, L79-L86 (2005). ISSN 0305-4470

Summary: The problem of the choice of tensor product decomposition in a system of two fermions with the help of Bogoliubov transformations of creation and annihilation operators is discussed. The set of physical states of the composite system is restricted by the superselection rule forbidding the superposition of fermions and bosons. It is shown that the Wootters concurrence is not the proper entanglement measure in this case. The explicit formula for the entanglement of formation is found. This formula shows that the entanglement of a given state depends on the tensor product decomposition of a Hilbert space. It is shown that the set of separable states is narrower than in the two-qubit case. Moreover, there exist states which are separable with respect to all tensor product decompositions of the Hilbert space.

MSC 2000:: *81P68 Quantum computation and quantum cryptography
81S05 Commutation relations (quantum theory)

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