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IBM Journal of Research and Development  
Volume 48, Number 1, Page 111 (2004)
Physics of information
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Some bipartite states do not arise from channels

by M. B. Ruskai
It is well known that the action of a quantum channel on a state can be represented, using an auxiliary space, as the partial trace of an associated bipartite state. Recently, it was observed that for the bipartite state associated with the optimal average input of the channel, the entanglement of formation is simply the entropy of the reduced density matrix minus the Holevo capacity. It is natural to ask if every bipartite state can be associated with some channel in this way. We show that the answer is negative.
Related Subjects: Information physics; Quantum theory and effects