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Sponsors

Pauli Center for Theoretical Studies

The Swiss National Science Foundation

ETH Zurich (Computer Science and Physics Department)

Quantum Science and Technology

CQT Singapore

QAP European Project

Sandia National Laboratories

Institute for Quantum Computing

id Quantique

Regularization and its discontents

Graeme Smith, IBM, Watson

The cornerstone of information theory is Shannon’s theorem, which shows that the capacity of a channel for noiseless communication is given by a simple optimization problem: it is the maximum mutual information that can be generated between input and output with a single use of the channel.  In the quantum setting, such “single-letter” formulas are few and far between.  The best expressions we have for quantum capacities involve optimizations of entropic quantities over an asymptotically large number of channel uses.  Such “regularized” formulas tell us very little.   The purpose of this talk is to give an overview of what we know about this need for regularization, when and why it happens, and what it means.  I will focus on the quantum capacity of a quantum channel, which is the case we understand best.