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Non-local Properties of Multi-particle Density Matrices
Linden, N.; Popescu, Sandu; Sudbery, A.
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 - ½ 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.
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