Abstract
The intuitiveness of the tensor network graphical language is becoming well knownthrough its use in numerical simulations using methods from tensor network algo-rithms. Recent times have also seen rapid progress in developing equations of motionto predict the time evolution of quantum entanglement [Nature Physics, 4(4):99,2008]. Here we cast these recent results into a tensor network framework and in do-ing so, construct a theory which exposes the topological equivalence of the evolutionof a family of entanglement monotones in arbitrary dimensions. This unification wasaccomplished by tailoring a form of channel state duality through the interpretationof graphical tensor network rewrite rules. The introduction of tensor network meth-ods to the theory of entanglement evolution opens the door to apply methods fromthe rapidly evolving area known as tensor network states.
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