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Thursday, October 28, 2010
12:30 PM - 2:00 PM
Theoretical Division Conference Room, TA-3, Building 123, Room 121.

Quantum Lunch

Minimum output entropy of quantum channels is hard to approximate

Aram Harrow
University of Washington

The headline result of this talk is that, based on plausible complexity-theoretic assumptions, many properties of quantum channels are computationally hard to approximate. These hard-to-compute properties include the minimum output entropy, the 1->p norms of channels, and their "regularized" versions, such as the classical capacity. The proof of this claim has two main ingredients. First, I show how many channel problems can be fruitfully recast in the language of two-prover quantum Merlin-Arther games (which I'll define during the talk). Second, the main technical contribution is a procedure that takes two copies of a multipartite quantum state and estimates whether or not it is close to a product state.

Host: Robin Blume-Kohout,