Entropy and energy in quantum networks
Abstract
Quantum channels are functions that map density matrices to density matrices. They can be used to describe a vast array of system environment interactions for quantum mechanical systems. The focus in quantum information theory lies on the study of the information content -- the quantum entropy -- of input and output system. The property of how much information a channel can convey is called capacity. When two quantum channels are combined they act on a bigger, possibly entangled state in parallel. The effects of entanglement on the capacity of a pair of channels have been widely studied. Still, recent work showed unexpected behavior. Hastings found that the capacities of two channels to transmit classical information does not simply add, but can exceed the sum of the individual quantum capacities, a property called superadditivity. We study Hastings' work and find estimates for how large the dimensions of such channels would have to be. The question of capacity relates to the behavior of quantum channels in extremal cases, when the output entropy is minimized. It is natural to wonder about the "standard" behavior of quantum channels and consider their average output entropy. We have studied this behavior in particular in cases where many relatively simple quantum channels act in parallel. When combining quantum channels in parallel, the parts of the system evolve independently of each other -- up to entanglement -- and only interact with the environment. Expanding on this…
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