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Nonlocal properties of multiparticle density matrices

Jan, 1998
13 pages
Published in:
  • Phys.Rev.Lett. 83 (1999) 243-247
e-Print:
DOI:
Report number:
  • NI-98001
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Abstract:
As far as entanglement is concerned, two density matrices of nn particles are equivalent if they are on the same orbit of the group of local unitary transformations, U(d1)×...×U(dn)U(d_1)\times...\times U(d_n) (where the Hilbert space of particle rr has dimension drd_r). We show that for nn greater than or equal to two, the number of independent parameters needed to specify an nn-particle density matrix up to equivalence is Πrdr2−∑rdr2+n−1\Pi_r d_r^2 - \sum_r d_r^2 + n - 1. For nn spin-12{1\over 2} 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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  • 13 pages RevTeX