The Diamond norm is a mathematical tool used primarily in quantum information theory to measure the distance between two quantum channels, or completely positive trace-preserving (CPTP) maps. It provides a way to quantify how distinguishable two quantum processes are when they are applied to quantum states.
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The diamond norm is the stabilized induced trace normFor a map on -dimensional inputs, an auxiliary space of dimension suffices. The tensor factor lets the norm detect how acts on one half of an entangled input.