Questions tagged [kraus-representation]

For questions relating to the Kraus decomposition of quantum channels.

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Is the composition of two extremal channels also extremal?

In this question, I follow the terminology and notation of the book of Watrous, most notably chapter two. Extremal channels An extremal channel $\Phi(X) \in C(\mathcal{X},\mathcal{Y})$ is a channel ...
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What do commuting quantum channels look like?

Consider two channels, $\Phi,\Psi\in\mathrm C(\mathcal X)$ acting on some space $\mathcal X$, and suppose they commute, that is, $$\Phi(\Psi(\rho))=\Psi(\Phi(\rho))$$ for all states $\rho$. Can ...
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Is a quantum channel reversible if all Kraus operators are proportional to unitaries?

In preskill's online lecture p.13, he stated that if a channel is reversible, i.e., $\varepsilon^{-1}\circ\varepsilon(\rho)=\rho$ for any $\rho$, then the kraus operator of the quantum channel must be ...
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What are examples of Kraus operators describing the process of control error?

Noise, such as photon loss or dephasing, is often described with Kraus operators. Are there examples of Kraus operators describing the process of control error?
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Kraus representation of a convex combination of CPT maps

Let $\Phi_1,\Phi_2$ be CPT maps with Kraus decomposition \Phi_1=\sum_{k=1}^{d_1}M_k\rho M_k^\dagger, \quad \Phi_2=\sum_{k=1}^{d_2} N_k\rho N_k^\dagger, \quad \text{s.t.} \quad \sum_{k=...
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Special properties of a channel whose Kraus decomposition contains Identity

I would like to know if there are any special properties of channels that permit a Kraus representation that includes an identity? That is, if I am given a Kraus representation of a CPTP map $\Phi$ ...
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Equivalent statement of the unitary freedom of Kraus operator?

There is a well-known form of the unitary freedom of Kraus operators, which can be found in Nielsen's book, stating that two sets of Kraus operators describe the same physical process of the system(...
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Implementing sum on Boolean with Grover algorithm

We are trying to implement a "sum over 4 booleans = k" in the spirit of Grover search. First, we have 4 qubits, one for each boolean q00, q01, q02, q03,; then 4 ...
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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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What is the Kraus representation of the quantum channel with Choi $\lambda |\phi^+\rangle \langle\phi^+| + (1-\lambda )|\phi^-\rangle \langle\phi^-|$?

This matrix $$c_{\lambda} = \lambda |\phi^+\rangle \langle\phi^+| + (1-\lambda )|\phi^-\rangle \langle\phi^-|$$ is the Choi–Jamiołkowski matrix of a quantum channel for any $\lambda \in [0,1]$. The ...
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Finding Kraus operators from the output density matrix

I have a question regarding Kraus operators. Any quantum channel can be written in terms of Kraus operators as $E(\rho)= \sum_{i=0}^n K_i \rho K_i^{\dagger}$ where $\rho$ is the initial density ...
I would like to understand an example of finding a noiseless subsystem of a quantum channel from the irreducible representation of its Kraus operators. Assume we have $2$ dephasing channels acting on ...