 Matrix product state as an unravelling of a completely positive map

ID: matrix-product-state-as-an-unravelling-of-a-completely-positive-map

A^{i}

define both the completely positive map

E (X) = \sum_{i} A^{i} X (A^{i})^{†}

and an MPS. Repeatedly retaining the Kraus label

i

purifies the channel output into the physical MPS chain; tracing those labels recovers repeated application of

E

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