# 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 are examples of quantum maps with complex eigenvalues?

Chapter 6 of Michael Wolf's notes (MichaelWolf/QChannelLecture.pdf) discuss the structure of the spectrum of quantum maps and channels. However, it seems like the only explicit example given in the ...
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### Why is error correction very different for circuits compared to channels?

Background Suppose one wishes to communicate information using a noisy channel $N$ instead of an ideal channel $I$. The general framework to communicate reliably is Take $n$ copies of $N$. For some ...
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### How to recover the original density matrix from the output of amplitude damping channel?

For amplitude damping, we have the below expression $$\xi(\rho)=E_0\rho{E_0}^\dagger + E_1\rho{E_1}^\dagger.$$ How can I perform a matrix inverse operation on $\xi(\rho)$ at the receiver to get back ...
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### How does the number of copies affect the diamond distance?

Suppose we are given two maps $\Phi$ and $\Psi$ such that $$\|\Phi-\Psi\|_{\diamond}\leqslant\varepsilon.$$ What can we say about $\left\|\Phi^{\otimes t}-\Psi^{\otimes t}\right\|_{\diamond}$? Is it ...
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### Creating a gate which have multiple register as an input

I'm trying to create a new gate in qiskit which the input is multiple register but the program output an error that says: ...
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### What is the adjoint of the depolarizing channel?

Consider the single qubit depolarizing noise channel given by $$\Phi(\rho) = \frac{\lambda}{d} \mathbb{I} + (1- \lambda) \rho.$$ What might be the adjoint $\Phi^{*}(\cdot)$ of this channel? In ...
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### Does a noiseless quantum channel violate no-cloning theorem?

A quantum channel is defined as CPTP map from Alice to Bob $\mathcal{N}: \mathcal{H}_A \to \mathcal{H}_B$. In particular, a noiseless quantum channel is such that $\mathcal{N}(\rho_A) = \rho_A$. My ...
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### What is the Bloch sphere representation of $\rho\to\mathcal{E}(\rho) = |+\rangle\langle+|ρ|+\rangle\langle+| + |−\rangle\langle−|ρ|−\rangle\langle−|$?

Suppose a projective measurement is performed on a single qubit in the basis $|+\rangle, |−\rangle$, where $|±\rangle \equiv (|0\rangle\pm |1\rangle)/\sqrt{2}$. In the event that we are ignorant of ...
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### What is the definition of twirled superoperator?

I am trying find the definition of twirled (super)operator. One such is Definition 2.3.16 on p. 33 of Christoph Dankert, Efficient Simulation of Random Quantum States and Operators. However, the ...
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