hw2sol_fa07 - C/CS/Phy191 Problem Set 2 Solutions Out:...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: C/CS/Phy191 Problem Set 2 Solutions Out: September 21, 2007 1. Alice is given as input a random bit a in and Bob a random bit b in . Without communicating with each other, Alice and Bob wish to output bits a out and b out respectively such that a in b in = a out + b out ( mod 2 ) . Prove that any classical protocol that Alice and Bob follow has success probability at most 3 / 4. Answer: If Alice and Bob both output 0 regardless of a in and b in , they achieve a success probability of 3 / 4. We need to show they can do no better. First, consider deterministic strategies. There are 2 4 = 16 deterministic strategies, one for each way in which the following strategy tables can be filled in with bits a out and b out : a in a ou 1 b in b out 1 Assume there is a deterministic strategy which succeeds with probability > 3 / 4 it must succeed in all four cases for a in , b in . Since complementing a out and b out does not change a out b out , we may assume the first entry in Alices table is 0 (otherwise, complement all entries in both tables). Considering the case a in = b in = 0 gives Bobs first entry is 0. From the case0 gives Bobs first entry is 0....
View Full Document

Page1 / 2

hw2sol_fa07 - C/CS/Phy191 Problem Set 2 Solutions Out:...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online