Journal Club Winter 2013
This quarter we will be focusing on Quantum Information Theory not Quantum Expanders, but the editing is yet to be completed so until then, confusion shall reign.
Place: Fridays at 1:30pm in CSE 674 ("the Irish room").
|Quantum Expanders: Motivation and Construction||Isaac||March 30|
|Continue Review||Kamil||April 6|
|Continue Review||Kamil||April 13|
|Quantum expanders from any classical Cayley graph expander||Kevin||April 20|
|Random Unitaries Give Quantum Expanders, Slides||Isaac||April 27|
|Quantum Expander States, Slides||Isaac||May 11|
|Classical and Quantum Tensor Product Expanders||Kevin||May 11|
|TPEs and Solovay-Kitaev||Kevin||May 25|
Review and Introduction
May 2010: Quantum Expanders: Motivation and Construction - Ben-Aroya, Schwartz, Ta-Shma
"We deﬁne quantum expanders in a natural way and give two constructions of quantum expanders, both based on classical expander constructions."
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
Jun 2007: Random Unitaries Give Quantum Expanders - M. B. Hastings
"We show that randomly choosing the matrices in a completely positive map from the unitary group gives a quantum expander. "
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. "
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."
Nov 2008: Efficient Quantum Tensor Product Expanders and k-designs - A. W. Harrow, R. A. Low
"we give an efficient construction of constant-degree, constant-gap quantum k-tensor product expanders."
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."
July 2004: Aspects of generic entanglement - Hayden, Leung, Winter
'"We study entanglement and other correlation properties of random states in high-dimensional bipartite systems."'
Jan 2007: Entropy and Entanglement in Quantum Ground States - M.B. Hastings
'"We prove that there exist gapped one-dimensional local Hamiltonians such that the entropy is exponentially large in the correlation length"'
Jun 2006: The mother of all protocols: Restructuring quantum information's family tree - Abeyesinghe, Devetak, Hayden, Winter
Oct 2010: From Low-Distortion Norm Embeddings to Explicit Uncertainty Relations and Efficient Information Locking - Fawzi, Hayden, Sen
Oct 2009: Non-additivity of Renyi entropy and Dvoretzky's Theorem - Aubrun, Szarek, Werner
Mar 2010: Hastings' additivity counterexample via Dvoretzky's theorem - Aubrun, Szarek, Werner
Jun 2011: Entanglement thresholds for random induced states - Aubrun, Szarek, Ye
Nov 2011: Towards the fast scrambling conjecture - Lashkari, Stanford, Hastings, Osborne, Hayden
Organizer(1): Isaac Crosson
Organizer(2): Kamil Michnicki
Faculty Advisor: Aram Harrow