[quantum-info] IQC Seminar Thursday Feb. 13 noon

[Matthew Fries]

Seminar

Institute for Quantum Computing

Thursday, 13 February 2014 at 12:00PM

QNC 0101

Applications of Information Theory in Direct Sum and Direct Product Problems

Penghui Yao

National University of Singapore

A fundamental question in complexity theory is how much resource is needed to solve k independent instances of a problem compared to the resource required to solve one instance. Suppose solving one instance of a problem with probability of correctness p, we require c units of some resource in a given model of computation. A direct sum theorem states that in order to compute k independent instances of a problem, it requires k times units of the resource needed to compute one instance. A strong direct product theorem states that, with o(k • c) units of the resource, one can only compute all the k instances correctly with probability exponentially small in k.
In this talk, I am going to present some of recent progress on direct sum and direct product theorems in the model of communication complexity and two-prover one-round games with information-theoretic approach. The talk is based on parts of my doctoral work.