Non-local properties of multi-particle density matrices

Details Non-local properties of multi-particle density matrices Non-local properties of multi-particle density matrices

1998-01-30

arxiv.org/abs/quant-ph/9801076v1

Phys.Rev.Lett.83:243-247,1999

Physics

Quantum Physics

13 pages RevTeX

Scientific paper

10.1103/PhysRevLett.83.243

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, $U(d_1)\times...\times U(d_n)$ (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 $\Pi_r d_r^2 - \sum_r d_r^2 + n - 1$. For $n$ spin-${1\over 2}$ 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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