Chasing Lecturer : Jaikumar Radhakrishnan Scribe : Sagnik Mukhopadhyay
نویسنده
چکیده
The index function problem is defined as follows. Alice has a string x distributed uniformly over {0, 1}n. Bob has an index i distributed uniformly over [n]. The goal for Bob is to guess xi when only one round of communication is allowed, i.e., Alice can send only one message to Bob. The naive protocol for this problem is that Alice sends all her bits to Bob. Then the message length is n. Our goal is to figure out whether we can reduce the message length using randomization and if so, how much we can reduce. Formally we want to have a lower bound on the message length. We will show this lower bound using information theoretic argument. Let us fix a deterministic protocol P that computes the index function. Suppose the error made by the deterministic protocol P is 12 − δ on uniform distribution over input. Let M is a random variable that represent the message send by Alice, which is determined by Alice’s input X = X1X2....Xn where Xis are independent.
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Privacy and Interaction in Quantum Communication Complexity and a Theorem about the Relative Entropy of Quantum States
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