# Journal Club Winter 2013

This season we will be focusing on Quantum Information Theory. Applications of classical information theory are ubiquitous in science and mathematics with applications ranging from characterizing ensembles of particles to answering how many bits can be sent reliably over a noisy channel. It is even useful as an estimation technique for gauging the difficulty of a problem, for instance, one may ask, how many bits are necessary to specify a quantum circuit acting on n bits(with bit flips Toffoli and Hadamard gates) and how does that compare to the number of bits required to specify a classical circuit? This question already puts a bound on the average quantum speed up attainable over classical circuits, e.g. there isn't enough information in the specification of constant depth quantum circuits to characterize an arbitrary reversible function on n-bits and so we conclude that there are classical functions that require more than constant quantum depth. Although this example is rather simple, it already gives the researcher some perspective about a very broad and difficult problem, that of finding quantum speed-ups. If classical information theory can quickly gives us insight into the classical resources needed for a task, perhaps quantum information theory would be equally useful in giving us insight into the quantum resources needed for a quantum task?

**Place and Time:** Thursday at 2:45pm in 6C-442 or in cyberspace via Google Hangouts.

## Schedule

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

Mixed State Entanglement and Quantum Error Correction | Kamil | 2/21 |

## Papers

### General Background

From Classical to Quantum Shannon Theory - A thorough and up-to-date (2012) free textbook by Mark Wilde.

Video lectures by Thomas Cover on classical information theory.

Nielson and Chuang, Quantum Computing and Quantum Information: Part III

### Papers

**April 1996:** Mixed State Entanglement and Quantum Error Correction - C. Bennett, D. DiVincenzo, J. Smolin, W. Wootters

**Sept 2003:** Secure key from bound entanglement K. Horodecki, M. Horodecki, P. Horodecki, J. Oppenheim

**July 2004:** Aspects of generic entanglement - P. Hayden, D. Leung, A. Winter

**Dec 2005:** Quantum state merging and negative information - M. Horodecki, J. Oppenheim, A. Winter

**June 2006:** The mother of all protocols: Restructuring quantum information's family tree - A. Abeyesinghe, I. Devetak, P. Hayden, A. Winter

**March 2007:** Symmetry implies independence - R. Renner

**Aug 2008:** The operational meaning of min- and max-entropy - R. Koenig, R. Renner, C. Schaffner

**Sept 2008:** Post-selection technique for quantum channels with applications to quantum cryptography - M. Christandl, R. Koenig, R. Renner

**April 2009:** A Generalization of Quantum Stein's Lemma - F. Brandao, M. Plenio

**Dec 2009:** Quantum Reverse Shannon Theorem - C. Bennett, I. Devetak, A. Harrow, P. Shor, A. Winter

**March 2010:** Hastings' additivity counterexample via Dvoretzky's theorem - G. Aubrun, S. Szarek, E. Werner

**March 2010:** Weak Decoupling Duality and Quantum Identification - P. Hayden, A. Winter

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

## Organizers

**Organizer:** Kamil Michnicki

**Wiki Page:** Isaac Crosson

**Faculty Advisor:** Aram Harrow