[quantum-info] PiQuDos seminar today - Graeme Smith - *ROOM CHANGE*

Daniel Brod dbrod at perimeterinstitute.ca
Wed Nov 16 13:02:36 EST 2016


Dear all,

Today's PIQuDos seminar by Graeme Smith has been moved to the *Bob room*,
at the same time (4pm).

On Wed, Nov 16, 2016 at 8:48 AM, Daniel Brod <dbrod at perimeterinstitute.ca>
wrote:

Reminder: Today at 4pm in the Time room, quantum information seminar by
Graeme Smith

***
Title: Uniform Additivity


Abstract:
Information theory establishes the fundamental limits on data transmission,
storage, and processing. Quantum information theory unites information
theoretic ideas with an accurate quantum-mechanical description of reality
to give a more accurate and complete theory with new and more powerful
possibilities for information processing. The goal of both classical and
quantum information theory is to quantify the optimal rates of
interconversion of different resources. These rates are usually
characterized in terms of entropies. However, nonadditivity of many
entropic formulas often makes finding answers to information theoretic
questions intractable. In a few auspicious cases, such as the classical
capacity of a classical channel, the capacity region of a multiple access
channel and the entanglement assisted capacity of a quantum channel,
additivity allows a full characterization of optimal rates. Here we present
a new mathematical property of entropic formulas, uniform additivity, that
is both easily evaluated and rich enough to capture all known quantum
additive formulas. We give a complete characterization of uniformly
additive functions using the linear programming approach to entropy
inequalities. In addition to all known quantum formulas, we find a new and
intriguing additive quantity: the completely coherent information. We also
uncover a remarkable coincidence---the classical and quantum uniformly
additive functions are identical; the tractable answers in classical and
quantum information theory are formally equivalent.
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