科研之友
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摘要
In this paper, we present the following quantum compression protocol 'P': Let rho, sigma be quantum states, such that S (rho parallel to sigma) (def) double under bar Tr(rho log rho - rho log sigma), the relative entropy between rho and sigma, is finite. Alice gets to know the eigendecomposition of rho. Bob gets to know the eigendecomposition of sigma. Both Alice and Bob know S(rho parallel to sigma) and an error parameter epsilon. Alice and Bob use shared entanglement and after communication of O((S(rho parallel to sigma) + 1)/epsilon(4)) bits from Alice to Bob, Bob ends up with a quantum state (rho) over tilde, such that F(rho, (rho) over tilde) >= 1-5 epsilon, where F(center dot) represents fidelity. This result can be considered as a non-commutative generalization of a result due to Braverman and Rao where they considered the special case when rho and sigma are classical probability distributions (or commute with each other) and use shared randomness instead of shared entanglement. We use P to obtain an alternate proof of a direct-sum result for entanglement assisted quantum one-way communication complexity for all relations, which was first shown by Jain et al.. We also present a variant of protocol P in which Bob has some side information about the state with Alice. We show that in such a case, the amount of communication can be further reduced, based on the side information that Bob has. Our second result provides a quantum analog of the widely used classical correlated-sampling protocol. For example, Holenstein used the classical correlated-sampling protocol in his proof of a parallel-repetition theorem for two-player one-round games.
- 出版日期2016-12
