Journal Club Spring 2012

This quarter we will be focusing on Quantum Expanders and Randomized Constructions.

People

Organizer(1): Isaac Crosson

Organizer(2): Kamil Michnicki (kpm3uw@gmail.com)

Faculty Advisor: Aram Harrow

Place

Friday 1:30pm in Computer Science, CSE 503.

Schedule

Subject	Speaker	Date
Introduction and Review	???	???
???	???	???

Papers

June 2003: Randomizing quantum states: Constructions and applications - Hayden, Leung, Shor, Winter
"The construction of a perfectly secure private quantum channel in dimension d is known to require 2 log d shared random key bits between the sender and receiver. We show that if only near-perfect security is required, the size of the key can be reduced by a factor of two."
http://arxiv.org/abs/quant-ph/0307104 , http://arxiv.org/abs/0802.4193

Sep 2004: Entanglement in Random Subspaces - Hayden
"The selection of random subspaces plays a role in quantum information theory analogous to the role of random strings in classical information theory."
http://arxiv.org/abs/quant-ph/0409157

Jun 2007: Random Unitaries Give Quantum Expanders - Hastings
"We show that randomly choosing the matrices in a completely positive map from the unitary group gives a quantum expander. "
http://arxiv.org/abs/0706.0556

Sep 2007: Quantum expanders from any classical Cayley graph expander - A. W. Harrow
"We give a simple recipe for translating walks on Cayley graphs of a group G into a quantum operation on any irrep of G. "
http://arxiv.org/abs/0709.1142 0709.1142

Apr 2008: Classical and Quantum Tensor Product Expanders - M. B. Hastings, A. W. Harrow
"We introduce the concept of quantum tensor product expanders. These are expanders that act on several copies of a given system, where the Kraus operators are tensor products of the Kraus operator on a single system."
http://arxiv.org/abs/0804.0011