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  Krauss operators for random unitary

+ 1 like - 0 dislike

Suppose I have a density matrix $\rho$ and I act on it with a unitary matrix that is chosen randomly, and with even probability, from $S = \{ H_1, H_2 \ldots H_N \}$. I want to write the operation on the density matrix in Krauss form:

$ \rho^{\prime} = \sum_i O_i \rho O^{\dagger}_i $

Since the operator is chosen evenly, the probability of choosing any $H_i$ is $\frac{1}{N}$. What would be my choices for $O_i$?

This post has been migrated from (A51.SE)

asked Mar 12, 2012 in Theoretical Physics by user442920 (90 points) [ revision history ]
edited Apr 19, 2014 by dimension10
Just a little quibble; you're using $H$ to represent a unitary. Upon first glance $H$ suggests Hamiltonian. I'd recommend turning your $H_i$ into $U_i$.

This post has been migrated from (A51.SE)

1 Answer

+ 3 like - 0 dislike

One obvious choice is $$O_i = \frac{1}{\sqrt{N}}H_i.$$ There are many other choices. Perhaps you could elaborate some.

This post has been migrated from (A51.SE)
answered Mar 12, 2012 by jonas (80 points) [ no revision ]
If you are interested in using the unitary freedom of the Krauss representation you can re-express the $O_i$'s as $O_i' = \sum_{j} u_{ij}O_j$. Where $u_{ij}$ are entries in a unitary matrix $U$.

This post has been migrated from (A51.SE)
THanks, the form suggested in the answer is the one I am interested in, though your comment is also useful!

This post has been migrated from (A51.SE)

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