##### Department of Mathematics,

University of California San Diego

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### Quantum Information and Computation

## Gilad Gour

#### University of Calgary

## Local additivity of the minimum entropy output of a quantum channel

##### Abstract:

An important open problem in quantum information concerns with the question whether entanglement between signal states can help in sending classical information over a quantum channel. Recently, Hastings proved that entanglement does help by finding a counter example for the long standing additivity conjecture that the minimum entropy output of a quantum channel is additive under taking tensor products. In this talk I will show that the minimum entropy output of a quantum channel is locally additive. Hastings' counter example for the global additivity conjecture makes this result somewhat surprising. In particular, it indicates that the non-additivity of the minimum entropy output is related to a global effect of quantum channels. I will end with a few related open problems.

Host: David Meyer

### November 20, 2012

### 10:30 AM

### AP&M 7321

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