Theory of Quantum Information and Computation Seminar: Ashwin NayakExport this event to calendar

Monday, November 7, 2016 — 11:30 AM EST

A proof of the quantum data processing inequality with a combinatorial flavour

Ashwin Nayak, Institute for Quantum Computing

The quantum data processing inequality (equivalently, the strong sub-additivity of von Neumann entropy) is a cornerstone of quantum information theory.  It has been proven in numerous ways, each proof highlighting different aspects of the property.We present a proof of the data processing inequality based on elementary probability theory and properties of quantum states. In fact, the property follows from a strengthening of the substate theorem [Jain, Radhakrishnan, Sen'02] in the asymptotic setting. We prove, via an explicit construction, that in the limit of large n, the relative entropy of n copies each of two quantum states \rho, \sigma essentially equals their smooth max-relative entropy. This is analogous to the relationship between Shannon entropy and min-entropy that arises in the context of the noiseless coding theorem.

This is joint work with Shitikanth Kashyap and Michael Saks.

Location 
QNC - Quantum Nano Centre
1201
200 University Avenue West

Waterloo, ON N2L 3G1
Canada

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