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Non-local Properties of Multi-particle Density Matrices

Linden, N.; Popescu, Sandu; Sudbery, A.

HPL-BRIMS-98-16

Keyword(s): quantum mechanics; quantum information; quantum non-locality; quantum entanglement

Abstract: As far as entanglement is concerned, two density matrices of n particles are equivalent if they are on the same orbit of the group of local unitary transformations, U (d1) X ??? X U (dn) (where the Hilbert space of particle r has dimension dr). We show that for n greater than or equal to two, the number of independent parameters needed to specify an n- particle density matrix up to equivalence is Πrd2r - Σrd2 r + n - 1. For n spin - particles we also show how to characterise generic orbits, both by giving an explicit parametrisation of the orbits and by finding a finite set of polynomial invariants which separate the orbits.

13 Pages

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