Salman Beigi, Amin Gohari
In this paper we study the benefit of entanglement in settings involving classical inputs, outputs, and communication channels from an information theoretic perspective. It is known that although (asymptotic) zero-error capacity of (point-to-point) classical channels may increase when the sender and receiver are provided with shared entanglement, permitting an asymptotically vanishing error eliminates this benefit. In contrast we show that in the correlation simulation problem, entanglement is strictly beneficial even with an asymptotically vanishing error requirement. To accomplish this we extend a special case of the recent result of Yassaee et al. to the entanglement-assisted setting. Further we argue that studying the benefit of entanglement in multi-terminal settings requires evaluation of expressions involving quantum auxiliary registers. This would require bounds on the dimension of the auxiliary quantum registers in a given expression. However no non-trivial technique for bounding the dimension of auxiliary quantum registers is known. To approach this problem we define the problem of quantum convexification. We show that quantum convexification is strictly reacher than the usual classical convexification. To prove this fact we develop new tools which might be useful for bounding the dimension of quantum registers in optimization problems involving an auxiliary quantum system.
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http://arxiv.org/abs/1207.3911
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