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