1202.3322 (Daniel Lehmann)

Some properties of n-party entanglement under LOCC operations    [PDF]

Daniel Lehmann

Nielsen characterized in full those 2-party quantum protocols of local
operations and classical communication that transform, with probability one, a
pure global initial state into a pure global final state. The present work
considers the generalization of Nielsen's characterization to n-party
protocols. It presents a sweeping generalization of the only if part of
Nielsen's result. The result presented here pertains also to protocols that do
not generate a final state for sure, it considers arbitrary mixed initial
states instead of pure states and n-party protocols for an arbitrary n. In this
very general setting, local operations and classical communication can never
decrease the expected spectra of the local mixed states in the majorization
ordering. In other terms, the local states can only become purer (weakly) in
expectation. The proof also provides an improvement on Nielsen's. The if part
of Nielsen's characterization does not generalize. This is shown by studying
the entanglement of three qubits. It is shown that one can find pure states of
a system of three qubits that are not equivalent under unitary local operations
but define local mixed states on all subparts of the system that have the same
spectra. Neither equivalence of pure states under local unitary operations nor
accessibility under LOCC operations among a system of three qubits can be
characterized by properties of the spectra of the local mixed states.

View original: http://arxiv.org/abs/1202.3322