[quantum-info] Next week's PIQuDos
Markus Mueller
mmueller at perimeterinstitute.ca
Fri Aug 31 08:58:30 EDT 2012
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
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