Quantum Information and Foundations of Quantum Mechanics
The Information-Disturbance Tradeoff and the Continuity of Stinespring's Representation
|aula DOTTORATO - MERCOLedì 17 MAGGIO ore 11.00|
|DIRK SCHLINGEMANN, Technical University of Braunschweig|
|Stinespring's dilation theorem is the basic structure theorem
for quantum channels: it states that any quantum channel arises from a unitary
evolution on a larger system. Here we prove a continuity theorem for Stinespring's
dilation: if two quantum channels are close in cb-norm, then it is always
possible to find unitary implementations which are close in operator norm,
with dimension-independent bounds.
This result generalizes Uhlmann's theorem from states to channels and allows to derive a formulation of the information-disturbance tradeoff in terms of quantum channels, as well as a continuity estimate for the no-broadcasting theorem. We briefly discuss further implications for quantum cryptography, thermalization processes, and the black hole information loss puzzle.