Dear All,
This weeks research day on Tuesday will be at the Computer Science
Building. I will present a recent paper by Horodecki et al. (see arXiv:
0902.0912).
Speaker: Dejan Dukaric
Title: Quantum Mutual Independence
Time: 5 pm
Place: IFW D44
Abstract:
We introduce the concept of mutual independence -- correlations shared
between distant parties which are independent of the environment. This
notion is more general than the standard idea of a secret key -- it is a
fully quantum and more general form of privacy. The states which possess
mutual independence also generalize the so called private states --
those that possess private key. We then show that the problem of
distributed compression of quantum information at distant sources can be
solved in terms of mutual independence, if free entanglement between the
senders and the receiver is available. Namely, we obtain a formula for
the sum of rates of qubits needed to transmit a distributed state
between Alice and Bob to a decoder Charlie. We also show that mutual
independence is bounded from above by the relative entropy modulo a
conjecture, saying that if after removal of a single qubit the state
becomes product, its initial entanglement is bounded by 1. We suspect
that mutual independence is a highly singular quantity, i.e. that it is
positive only on a set of measure zero; furthermore, we believe that its
presence is seen on the single copy level. This appears to be born out
in the classical case.
Cheers,
Dejan