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We investigate local and nonlocal entanglement of particle pairs induced bydirect and crossed Andreev reflections at the interfaces between asuperconductor and two normal conductors. It is shown theoretically that bothlocal and nonlocal entanglement can be quantified by concurrence and detectedfrom the violation of a Bell inequality of spin current correlators, which aredetermined only by normal reflection and Andreev reflection eigenvalues. Thereexists a one-to-one correspondence between the concurrence and the maximalBell-CHSH parameter in the tunneling limit

Local and nonlocal entanglement for quasiparticle pairs induced by Andreev reflection