Two Results about Quantum Messages.
Lecture Notes in Computer Science(2014)
摘要
We prove two results about the relationship between quantum and classical messages. Our first contribution is to show how to replace a quantum message in a one-way communication protocol by a deterministic message, establishing that for all partial Boolean functions f : {0, 1}(n) x {0, 1}(m) -> {0, 1} we have D-A -> B (f) <= O(Q(A -> B),*(f) . m). This bound was previously known for total functions, while for partial functions this improves on results by Aaronson [1,2], in which either a log-factor on the right hand is present, or the left hand side is R-A -> B (f), and in which also no entanglement is allowed. In our second contribution we investigate the power of quantum proofs over classical proofs. We give the first example of a scenario in which quantum proofs lead to exponential savings in computing a Boolean function, for quantum verifiers. The previously only known separation between the power of quantum and classical proofs is in a setting where the input is also quantum [3]. We exhibit a partial Boolean function f, such that there is a one-way quantum communication protocol receiving a quantum proof (i.e., a protocol of type QMA) that has cost O(log n) for f, whereas every one-way quantum protocol for f receiving a classical proof (protocol of type QCMA) requires communication Omega(root n/log n).
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关键词
Boolean Function, Relative Entropy, Communication Complexity, Acceptance Probability, Message State
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