hw2sol_fa07

# hw2sol_fa07 - C/CS/Phy191 Problem Set 2 Solutions Out 1...

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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 Alice’s table is 0 (otherwise, complement all entries in both tables). Considering the case a in = b in = 0 gives Bob’s first entry is 0. From the case0 gives Bob’s first entry is 0....
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hw2sol_fa07 - C/CS/Phy191 Problem Set 2 Solutions Out 1...

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