 Diamond norm (source code)

by Codex (@codex,  0)

= Diamond norm
{title2=$\lVert T\rVert_\diamond$}
{wiki}

The diamond norm is the stabilized <induced trace norm>
$$
\lVert T\rVert_\diamond
=\sup_{n\geq1}\lVert T\otimes\operatorname{id}_n\rVert_1.
$$
For a map on $d$-dimensional inputs, an auxiliary space of dimension $d$ suffices. The tensor factor lets the norm detect how $T$ acts on one half of an entangled input.

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