5,669 research outputs found
Entropy Production of Doubly Stochastic Quantum Channels
We study the entropy increase of quantum systems evolving under primitive,
doubly stochastic Markovian noise and thus converging to the maximally mixed
state. This entropy increase can be quantified by a logarithmic-Sobolev
constant of the Liouvillian generating the noise. We prove a universal lower
bound on this constant that stays invariant under taking tensor-powers. Our
methods involve a new comparison method to relate logarithmic-Sobolev constants
of different Liouvillians and a technique to compute logarithmic-Sobolev
inequalities of Liouvillians with eigenvectors forming a projective
representation of a finite abelian group. Our bounds improve upon similar
results established before and as an application we prove an upper bound on
continuous-time quantum capacities. In the last part of this work we study
entropy production estimates of discrete-time doubly-stochastic quantum
channels by extending the framework of discrete-time logarithmic-Sobolev
inequalities to the quantum case.Comment: 24 page
Instruments and channels in quantum information theory
While a positive operator valued measure gives the probabilities in a quantum
measurement, an instrument gives both the probabilities and the a posteriori
states. By interpreting the instrument as a quantum channel and by using the
typical inequalities for the quantum and classical relative entropies, many
bounds on the classical information extracted in a quantum measurement, of the
type of Holevo's bound, are obtained in a unified manner.Comment: 12 pages, revtex
Quantum measurements and entropic bounds on information transmission
While a positive operator valued measure gives the probabilities in a quantum
measurement, an instrument gives both the probabilities and the a posteriori
states. By interpreting the instrument as a quantum channel and by using the
monotonicity theorem for relative entropies many bounds on the classical
information extracted in a quantum measurement are obtained in a unified
manner. In particular, it is shown that such bounds can all be stated as
inequalities between mutual entropies. This approach based on channels gives
rise to a unified picture of known and new bounds on the classical information
(Holevo's, Shumacher-Westmoreland-Wootters', Hall's, Scutaru's bounds, a new
upper bound and a new lower one). Some examples clarify the mutual
relationships among the various bounds.Comment: 29 pages, 2 figures, uses qic.st
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