R. Prabhu, Arun Kumar Pati, Aditi Sen De, Ujjwal Sen
We show that the classical capacity of quantum states, as quantified by its ability to perform dense coding, is a monogamous quantity, for arbitrary pure or mixed three-party states of arbitrary dimensions. The monogamy behavior is strict, in the sense that if a sender has a quantum advantage in dense coding to one of the two receivers, she must necessarily have no quantum advantage for the other receiver. We also generalize it to multi-port classical capacities of multi-party (more than three-party) quantum states in arbitrary dimensions. This strict monogamy relation is independent of the content and distribution of entanglement in the multipartite state. In the scenario of two senders and a single receiver, we show that if two of them wish to send classical information to a single sender independently, then the corresponding dense coding capacities satisfy the monogamy relation, similar to the relation for quantum correlations.
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http://arxiv.org/abs/1203.4114
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