1 research outputs found
Radon-Nikodym derivatives of quantum operations
Given a completely positive (CP) map , there is a theorem of the
Radon-Nikodym type [W.B. Arveson, Acta Math. {\bf 123}, 141 (1969); V.P.
Belavkin and P. Staszewski, Rep. Math. Phys. {\bf 24}, 49 (1986)] that
completely characterizes all CP maps such that is also a CP map. This
theorem is reviewed, and several alternative formulations are given along the
way. We then use the Radon-Nikodym formalism to study the structure of order
intervals of quantum operations, as well as a certain one-to-one correspondence
between CP maps and positive operators, already fruitfully exploited in many
quantum information-theoretic treatments. We also comment on how the
Radon-Nikodym theorem can be used to derive norm estimates for differences of
CP maps in general, and of quantum operations in particular.Comment: 22 pages; final versio