Workshop on

Quantum Information and Foundations of Quantum Mechanics

Quantum Channels with Memory

aula DOTTORATO - MERCOLedì 17 MAGGIO ore 10.00
  DENNIS KRETSCHMANN, Cambridge University

Dennis is a PhD student in Reinhard Werner's quantum information theory group at TU Braunschweig. He currently spends an enjoyable year away from home at Cambridge University, where he is a member of Artur Ekert's Centre for Quantum Computation at the Department of Applied Mathematics and Theoretical Physics. His current work lies mainly in abstract quantum information theory, in particular channels and their capacity for classical and quantum information transfer.

Dennis Kretschmann
  Any processing of quantum information, be it storage or transfer, can be represented as a quantum channel: a completely positive and trace-preserving map that transforms states on the sender's end of the channel into states on the receiver's end. Until now most of the work on quantum channels has concentrated on {memoryless} channels, which are characterized by the requirement that successive channel inputs are acted on independently.
However, in many real-world applications the assumption of having uncorrelated noise channels cannot be justified, and {memory effects} need to be taken into account.
In this seminar talk I will present a general model to describe such memory effects. Albeit relatively simple, this model can be shown to encompass every stationary causal physical process, and thus is completely general.
I will then introduce capacities for the transfer of classical and quantum information over memory channels, and discuss some simple examples in which these can be easily evaluated.
For the general case, I will present entropic upper bounds on the various capacities. For so-called {forgetful} channels, in which the effect of the initializing memory dies out as time increases, these bounds can be saturated. I will also show that generic memory channels are forgetful, and briefly summarize what is known about non-forgetful channels.