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Prove that if Kraus operators of $\Phi$ form an ONB then $\Phi$ is the replacement map

Distraction The matrix $P$ is a distraction, because the $dd'$ matrices $A_k$ are an orthonormal basis with respect to the inner product $\langle A,B\rangle_P:=\mathrm{tr}(PA^\dagger B)$ if and only ...
Adam Zalcman's user avatar
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4 votes
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How many free real parameters in a general CPTP map?

An easier way of counting is to consider the Choi state: It is a hermitian $d_Ad_B\times d_Ad_B$ matrix, and thus has $(d_Ad_B)^2$ real parameters. The condition that the reduced state of $A$ is the ...
Norbert Schuch's user avatar
2 votes

Prove that if Kraus operators of $\Phi$ form an ONB then $\Phi$ is the replacement map

This solution uses the spectral theorem and some elementary linear algebra computations. If you let $P = \sum_{i = 1}^{d'} \lambda_i \vert{\psi_i}\rangle\langle{\psi_i}\vert$ be the spectral ...
user2533488's user avatar
3 votes
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Affine transformation of the Bloch sphere to Kraus representation of qubit channels

TL;DR: The given form of the channel is essentially an obscured way of writing down the channel's Pauli transfer matrix. One set of Kraus operators coincides (up to vectorization) with the ...
Adam Zalcman's user avatar
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0 votes

Why is dual-rail encoding called an error-detecting code for amplitude damping?

I don't think the maths reasoning is really rigorous here (neither it is from the physics point of view), even if you get the right answer \begin{alignat*}{1} \varepsilon_{AD}\otimes \varepsilon_{AD}(\...
Pierre-Paul T.'s user avatar

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