2 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
Minimum error discrimination of Pauli channels
We solve the problem of discriminating with minimum error probability two
given Pauli channels. We show that, differently from the case of discrimination
between unitary transformations, the use of entanglement with an ancillary
system can strictly improve the discrimination, and any maximally entangled
state allows to achieve the optimal discrimination. We also provide a simple
necessary and sufficient condition in terms of the structure of the channels
for which the ultimate minimum error probability can be achieved without
entanglement assistance. When such a condition is satisfied, the optimal input
state is simply an eigenstate of one of the Pauli matrices.Comment: 8 pages, no figure