# POVM and quantum information

1. Jan 19, 2016

### aaaa202

Hi everyone I need help understanding the lines on the attached picture.

In the proof of corollary 14 how does it follow from corollary 13 that:

Λ(X) = ∑li><il Tr[KijXKij]

I think what has been done is take a partial trace over the system HB, but what exactly is the effect of this? It says that it is when the effect is not on the outcome measurement, so does the system carry information about the outcome of the measure while the system HA contains information about something else.

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2. Jan 21, 2016

### Staff: Mentor

Don't forget that $H_B = ℂ$ is one-dimensional in Cor. 14.