Timeline for Is a probabilistic implementation of unitaries invertible?
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| Aug 27 at 0:00 | comment | added | user196574 | I think you might be misunderstanding the question. The question is whether the map $A \to \sum_{i=1} p_i U_i A U_i^\dagger$ is always invertible for unitary $U_i$. (I use $^\dagger$ for Hermitian conjugate and $^*$ for complex conjugation.) As I show in my answer, it is not always invertible. Phrased a different way, the question is not about averages of $U_i$ but rather about averages of $U_i^* \otimes U_i$. I believe your answer is about averages of $U_i$. | |
| Aug 26 at 19:03 | history | answered | Michael Hardy | CC BY-SA 4.0 |