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Nonlocal Properties of Multiparticle Density Matrices
Linden, N.; Popescu, Sandu; Sudbery, A.
HPLBRIMS9816
Keyword(s): quantum mechanics; quantum information; quantum nonlocality; 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
(d_{1}) X ??? X U (d_{n}) (where the Hilbert space
of particle r has dimension d_{r}). 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 Π_{r}d^{2}r
 Σ_{r}d^{2} _{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.
13 Pages
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