Questions tagged [kraus-representation]

For questions relating to the Kraus decomposition of quantum channels.

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How does the invertibility of a quantum map reflect on its Kraus operators?

Consider a quantum map $\Phi\in\mathrm T(\mathcal X)$, that is, a linear operator $\Phi:\mathrm{Lin}(\mathcal X)\to\mathrm{Lin}(\mathcal X)$ for some finite-dimensional complex vector spaces $\mathcal ...
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What's a "natural" way to show that, for unital channels, $\Phi(X)=X$ iff $[X,A_a]=0$ for all Kraus operators $A_a$?

This is a statement proved in Watrous, Theorem 4.25, page 229 of the online version. Let $\Phi\in\mathrm C(\mathcal X)$ be a unital channel with Kraus representation $\Phi(X)=\sum_a A_a X A_a^\dagger$....
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How to compute the capacity of a quantum channel from its Kraus operators?

Is there a working rule to compute the capacity of a quantum channel described by a set of Kraus operators $\{K_i\}$?
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How is $I(\rho^{QC})=I_{CC}(\rho^{QC})$

On page 3 of this paper, for the proof of theorem 1, it states that, using Lemma 2 from the previous page, that if $$I(\Lambda_{A}\otimes\Gamma_{B})[\rho]=I(\rho))$$ then there exists $\Lambda_{A}^{*}$...
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Qiskit function phase_amplitude_damping_error

I am reading about the noise models that can be simulated in Qiskit and I found out the phase_amplitude_damping_error function. I read about it and it seems to be a function that simulates a combined ...
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Affine Map of the Bloch sphere

I am referring to Equation (8.89) to (8.92) in Chapter 8 of "Quantum Computing and Information 10th Anniversary Edition" by Nielsen and Chuang. This section deals with the geometric picture of single ...