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Multiplicativity of completely bounded p-norms implies a strong converse for entanglement-assisted capacity

Presented by: 
M Wilde Louisiana State University
Thursday 12th December 2013 - 14:00 to 15:00
INI Seminar Room 1
The fully quantum reverse Shannon theorem establishes the optimal rate of noiseless classical communication required for simulating the action of many instances of a noisy quantum channel on an arbitrary input state, while also allowing for an arbitrary amount of shared entanglement of an arbitrary form. Turning this theorem around establishes a strong converse for the entanglement-assisted classical capacity of any quantum channel. The present work proves the strong converse for entanglement-assisted capacity by a completely different approach. Namely, we exploit the recent entanglement-assisted "meta-converse" theorem of Matthews and Wehner, several properties of the recently established sandwiched Renyi relative entropy (also referred to as the quantum Renyi divergence), and the multiplicativity of completely bounded p-norms due to Devetak et al. The proof here demonstrates the extent to which the Arimoto approach can be helpful in proving strong converse theorems, it provides an operational relevance for the multiplicativity result of Devetak et al., and it adds to the growing body of evidence that the sandwiched Renyi relative entropy is the correct quantum generalization of the classical concept for all alpha > 1. This is joint work with Manish K. Gupta and is available as arXiv:1310.7028.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons