Physics – Quantum Physics
Scientific paper
2004-01-12
Phys. Rev. A. 70, 012109 (2004)
Physics
Quantum Physics
18 pages, Latex; revised version: Section 3.2 rewritten, new Theorems added, reference [1] corrected. To appear on Phys.Rev.A
Scientific paper
10.1103/PhysRevA.70.012109
We relate the notion of entanglement for quantum systems composed of two identical constituents to the impossibility of attributing a complete set of properties to both particles. This implies definite constraints on the mathematical form of the state vector associated with the whole system. We then analyze separately the cases of fermion and boson systems, and we show how the consideration of both the Slater-Schmidt number of the fermionic and bosonic analog of the Schmidt decomposition of the global state vector and the von Neumann entropy of the one-particle reduced density operators can supply us with a consistent criterion for detecting entanglement. In particular, the consideration of the von Neumann entropy is particularly useful in deciding whether the correlations of the considered states are simply due to the indistinguishability of the particles involved or are a genuine manifestation of the entanglement. The treatment leads to a full clarification of the subtle aspects of entanglement of two identical constituents which have been a source of embarrassment and of serious misunderstandings in the recent literature.
Ghirardi GianCarlo
Marinatto Luca
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