Questions tagged [kraus-representation]
For questions relating to the Kraus decomposition of quantum channels.
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Does $N(U\rho U^\dagger)=U' N(\rho)U'^\dagger$ for unitaries $U,U'$ and a channel $N$ imply $UK_i=K_i U'$?
Let $H_A, H_B$ be Hilbert spaces and let a channel $N_{A\rightarrow B}$ be a CPTP map between them. If there exist that unitaries $U\in H_A$ and $U'\in H_B$ such that for all $\rho\in H_A$
$$N(U\rho U^...
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Are peripheral eigenvalues of a completely positive map always semisimple?
It is known that all peripheral eigenvalues (i.e. all eigenvalues $\lambda\in\mathbb C$ such that $|\lambda|$ equals the spectral radius) of positive trace-preserving or positive unital maps are ...
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Are Stinespring unitaries that give rise to the same channel locally unitarily equivalent?
It is well known that for if any two linear maps $V_1,V_2:\mathbb C^n\to\mathbb C^k\otimes\mathbb C^m$ (isometry or not) satisfy
$$
{\rm tr}_{\mathbb C^m}(V_1(\cdot)V_1^\dagger)={\rm tr}_{\mathbb C^m}(...
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Given $\Psi$ completely positive when do there exist $K_1,K_2$ such that $K_2\Psi(K_1^\dagger(\cdot)K_1)K_2^\dagger$ is also trace preserving?
In quantum information it occasionally happens that one ends up with a completely positive but not yet trace-preserving map $\Psi$ which one wants to make trace preserving somehow; this often comes up ...
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How does measuring a density matrix give Kraus operators?
I am trying to complete this exercise regarding noisy channels. I need to measure a density matrix to get the Kraus operators. However, if I measure, I only get scalars. Can someone please explain how ...
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Why do we need/have the operator sum representation (Kraus representation)?
I am reading through Nielsen & Chuang, and I am on the section about operator sum representation. They performed this derivation.
Why is it important and useful for us to bundle together the ...
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Why is the Choi matrix different from the analytic form for a depolarizing channel?
I'm currently trying to implement the depolarizing channel on qiskit. But, as I see in my calculation it doesn't match with the qiskit aer_noise.
So, for the Depolarizing Channel we got :
$$
\mathcal{...
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What are kraus operators of a qubit interacting a thermal environment?
Suppose a qubit that interacting a thermal environment. The thermal environment can be a thermal field for example. What is the kraus operators for this case?
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Is the trace of a positive map always positive?
Obviously, positive semi-definite operators always admit a positive trace as ${\rm tr}(A)=\|A\|_1\geq 0$ whenever $A\geq 0$. This motivates the following "lifted" question:
Given any ...
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What is the meaning of $\sum_i K_iK_i^\dagger$ for a quantum channel with Kraus operators $K_i$?
Let a channel $N$ be given in terms of its Kraus operators $K_i$ as
$$N(\rho) = \sum_i K_i\rho K_i^\dagger.$$
Is the sum $\sum_i K_iK_i^\dagger$ a meaningful quantity? I know that $\sum_i K_i K_i^\...
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Counterexamples in quantum information theory
As was already asked about in this phys.SE question many years ago—which, sadly, got closed and never received an answer—is there a collection of counterexamples in quantum information theory, "...
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How to get the Kraus decomposition of the amplitude damping channel from its Choi?
I found going from the Choi-matrix of a quantum channel to the Choi-Kraus decomposition a bit difficult. I know that it follows from the eigen-decomposition of the Choi-matrix. But I struggle with ...
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How to model the IBM quantum errors?
I'm conducting a study of the quantum channel errors, and a question has arisen: Is it possible to model the errors of an IBM quantum computer with Kraus operators?
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Find the Kraus operators for the amplitude damping channel from its isometric representation
I am currently learning about quantum channels and am sadly stuck at a rudimentary problem, where I don't understand how to find the Kraus matrices of a quantum channel.
The amplitude damping channel ...
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How many free real parameters in a general CPTP map?
The question is how many free real parameters a general CPTP map can maximally have.
Let's assume the CPTP map $\Phi:L(\mathcal{H}_A) \rightarrow L(\mathcal{H}_B)$ is given in the Kraus representation
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