Journal Club Spring 2012
This quarter we will be focusing on Quantum Expanders and Randomized Constructions.
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