# Questions tagged [quantum-operation]

For questions about completely positive (CP) linear maps between quantum states. Can also be used for trace-preserving CP maps (quantum channels). For questions about unitary operations, please use quantum-gate instead.

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### What is a covariant quantum channel?

A novice to this topic, I am trying to understand the notion of (irreducible) Covariant Quantum Channels. This article provides a definition that is not very "physical". My question: What ...
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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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### How are eavesdroppers detected when using BB84 in the presence of noise?

I would like to expand upon this question: What is the probability of detecting Eve's tampering, in BB84? Let's say that when the receiver (colloquially referred to as Bob) receives a qubit and ...
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### How to use the Kraus operators to represent the total density matrix instead of the reduced one?

In Nielsen's book, the Kraus operator can be attained by trace out the enviroment: $$\operatorname{Tr}_{\rm env}[\hat{U}(|\psi\rangle\otimes|0\rangle)(\langle\psi|\otimes\langle 0|)\hat{U}^\dagger].$$...
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### Permutation covariant channels and their Stinespring dilations

I am interested in a quantum channel from $A^{\otimes n}$ to $B^{\otimes n}$ denoted as $N_{A^{\otimes n} \rightarrow B^{\otimes n}}(\cdot)$. Let $\pi(\cdot)$ be a permutation operation among the $n$ ...
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### Prove that a Bell state is invariant under the single-qubit gate acting on both qubits

I have a Bell state ${\Psi}^{-}= \frac{1}{\sqrt2} (|01\rangle - |10\rangle).$ How can I prove that this state is invariant (up to a global phase), when doing the same unitary $U$ on each qubit? That ...
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