# 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").

## Contents

## Schedule

Subject | Speaker | Date |
---|---|---|

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 |

Jun 1 | ||

## Papers

### 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."*

http://theoryofcomputing.org/articles/v006a003/

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

### Expander Constructions

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. "*

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

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."*

http://arxiv.org/abs/0811.2597

### Entanglement

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

July 2004: **Aspects of generic entanglement** - Hayden, Leung, Winter

'"We study entanglement and other correlation properties of random states in high-dimensional bipartite systems."'

http://arxiv.org/abs/quant-ph/0407049

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"'

http://arxiv.org/abs/cond-mat/0701055

### Additional Topics

Jun 2006: **The mother of all protocols: Restructuring quantum information's family tree** - Abeyesinghe, Devetak, Hayden, Winter

http://arxiv.org/abs/quant-ph/0606225

Oct 2010: **From Low-Distortion Norm Embeddings to Explicit Uncertainty Relations and Efficient Information Locking** - Fawzi, Hayden, Sen

http://arxiv.org/abs/1010.3007

Oct 2009: **Non-additivity of Renyi entropy and Dvoretzky's Theorem** - Aubrun, Szarek, Werner

http://arxiv.org/abs/0910.1189

Mar 2010: **Hastings' additivity counterexample via Dvoretzky's theorem** - Aubrun, Szarek, Werner

http://arxiv.org/abs/1003.4925

Jun 2011: **Entanglement thresholds for random induced states** - Aubrun, Szarek, Ye

http://arxiv.org/abs/1106.2264

Nov 2011: **Towards the fast scrambling conjecture** - Lashkari, Stanford, Hastings, Osborne, Hayden

http://arxiv.org/abs/1111.6580

## Organizers

**Organizer(1):** Isaac Crosson

**Organizer(2):** Kamil Michnicki

**Faculty Advisor:** Aram Harrow