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Why $\sqrt{\rho} = P \sqrt{\rho}$ in the proof of quantum error correction conditions in Nielsen & Chuang?

Recall from the sentence immediately preceding $(10.20)$ that $\rho$ is a state in the code subspace $C$ and from the statement of theorem $10.1$ that $P$ is a projector onto $C$. We will show that $\...
Adam Zalcman's user avatar
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Why $\sqrt{\rho} = P \sqrt{\rho}$ in the proof of quantum error correction conditions in Nielsen & Chuang?

$\rho$ is a state in the code. $P$ is the projector onto the codespace. That means (by definition) that for any state $|\psi\rangle$ in the code, $P|\psi\rangle=|\psi\rangle$. $\rho$ is one such state ...
DaftWullie's user avatar
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How is the $\beta$-matrix interpreted in single qubit QPT?

I am suggesting a way of indexing the 16 x 16 $\beta$ matrix, but I am not sure if it corresponds to your Eq(*) \begin{equation} \beta = \frac{1}{4} \left[ \begin{matrix} \beta_{11}^{00} & \beta_{...
Sachindra Kumar's user avatar
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Question about Nielson & Chuang Problem 9.2

I have a sketch of ideas, but haven't buttoned up all the details into a proof so use it as a set of hints. Intuition: Kraus operators have a unitary freedom, thus you can get the next set of Kraus ...
Balint Pato's user avatar

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