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Double Dilation $
eq$ Double Mixing (extended abstract) | | Maaike Zwart
; Bob Coecke
; | | Date: |
2 Mar 2018 | | Abstract: | Density operators are one of the key ingredients of quantum theory. They can
be constructed in two ways: via a convex sum of ’doubled kets’ (i.e. mixing),
and by tracing out part of a ’doubled’ two-system ket (i.e. dilation). Both
constructions can be iterated, yielding new mathematical species that have
already found applications outside physics. However, as we show in this paper,
the iterated constructions no longer yield the same mathematical species.
Hence, the constructions ’mixing’ and ’dilation’ themselves are by no means
equivalent. Concretely, when applying the Choi-Jamiolkowski isomorphism to the
second iteration, dilation produces arbitrary symmetric bipartite states, while
mixing only yields the disentangled ones. All results are proven using
diagrams, and hence they hold not only for quantum theory, but also for a much
more general class of process theories. | | Source: | arXiv, 1803.0700 | | Services: | Forum | Review | PDF | Favorites | |
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