Hi all,
next week, we have a talk by Karol Zyczkowski on Wednesday at 4pm in
the Time Room.
Best wishes,
Markus
Title: Entropic uncertainty relations for quantum operations
Speaker: Karol Zyczkowski (Jagiellonian University, Cracow, Poland)
Abstract:
We analyze the set of discrete quantum operations acting on an
N-level system from the entropic point of view.
Spectral properties of an arbitrary matrix can be characterized by
the entropy of its rescaled singular values. Any quantum operation
can be described by the associated dynamical matrix or by the
corresponding superoperator. The entropy of the dynamical matrix
describes the degree of decoherence introduced by the map, while
the entropy of the superoperator characterizes the a priori
knowledge of the receiver of the outcome of a quantum channel
$\Phi$.
We prove that for any map acting on a N-dimensional quantum system
the sum of both entropies is not smaller than $\ln N$. For any
bistochastic map this lower bound reads $2\ln N$. We investigate
also the corresponding Renyi entropies, provide an upper bound for
their sum and analyze entanglement of the bi-partite quantum state
associated with the channel.
Date: September 05, 2012 - 4:00 pm
Series: Perimeter Institute Quantum Discussions
Location: Time Room