8

You cannot always find such a Kraus decomposition. Notice that any CPTP map $\mathcal E$ which does have a decomposition as a probabilistic mixture unitaries is unital, which is to say that it maps the identity to the identity, and in particular it maps the maximally mixed state to the maximally mixed state: $$ \mathcal E(\tfrac{1}{d} \mathbf 1) = \tfrac{1}{...


3

I would say the most important classes are concatenated codes, topological codes and LDPC codes. But it depends on how one defines 'classes', as one could also talk of CSS vs non-CSS, stabilizer vs subsystem. In any case, I'll explain my three chosen 'classes'. Concatenated codes are used in cases where we know a code that has a finite code distance (and ...


2

In schemes like E91, the idea behind using an entangled state is that: in a particular measurement basis (for both parties), the measurement outcomes are perfectly correlated but completely random (50:50 outcomes). you can perform a Bell test on the state to verify its nature. Using a maximally entangled state gives you the property of the 50:50 outcomes (...


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