[quantum-info] Next week's PIQuDos

Markus Mueller markus14m at gmail.com
Fri May 11 10:30:34 EDT 2012


Hi all,

next week, we have a talk by Robert Koenig on Wednesday at 4pm in the 
Time Room.

Best wishes,
Markus



Title: *The entropy power inequality for quantum systems*
Speaker: Robert Koenig ( IBM Watson Research Lab)

Abstract:
When two independent analog signals, $X$ and $Y$ are added together 
giving $Z=X+Y$, the entropy of $Z$, $H(Z)$, is not a simple function of 
the entropies $H(X)$ and $H(Y)$, but rather depends on the details of 
$X$ and $Y$'s distributions.  Nevertheless, the entropy power inequality 
(EPI), which states that $e^{2H(Z)} \geq e^{2H(X)} +e^{2H(Y)}$, gives a 
very tight restriction on the entropy of $Z$. This inequality has found 
many applications in information theory and statistics.  The quantum 
analogue of adding two random variables is the combination of two 
independent bosonic modes at a beam splitter. The purpose of this talk 
is to give an outline of the proof of two separate generalizations of 
the entropy power inequality to the quantum regime.  These inequalities 
provide strong new upper bounds for the classical capacity of quantum 
additive noise channels, including quantum analogues of the additive 
white Gaussian noise channels.

Our proofs are similar in spirit to standard classical proofs of the 
EPI, but some new quantities and ideas are needed in the quantum 
setting. Specifically, we find a new quantum de Bruijin identity 
relating entropy production under diffusion to a divergence-based 
quantum Fisher information. Furthermore, this Fisher information 
exhibits certain convexity properties in the context of beam splitters.

This is joint work with Graeme Smith.



Date: May 16, 2012 - 4:00 pm
Series: Perimeter Institute Quantum Discussions
Location: Time Rm


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