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