1202.3329 (Daniel Lehmann)

Measurements and majorization    [PDF]

Daniel Lehmann

Majorization is an outstanding tool to compare the purity of mixed states or
the amount of information they contain and also the degrees of entanglement
presented by such states in tensor products. States are compared by their
spectra and majorization defines a partial order on those. This paper studies
the effect of measurements on the majorization relation among states. It, then,
proceeds to study the effect of local measurements on the agents sharing an
entangled global state. If the result of the measurement is recorded, Nielsen
and Vidal showed that the expected spectrum after any P.O.V.M. measurement
majorizes the initial spectrum, i.e., a P.O.V.M. measurement cannot, in
expectation, reduce the information of the observer. A new proof of this result
is presented and, as a consequence, the only if part of Nielsen's
characterization of LOCC transformations is generalized to n-party
entanglement. If the result of a bi-stochastic measurement is not recorded, the
initial state majorizes the final state, i.e., no information may be gained by
such a measurement. This strengthens a result of A. Peres. In the n-party
setting, no local trace preserving measurement by Alice can change the local
state of another agent.

View original: http://arxiv.org/abs/1202.3329