# Tag Info

• 4,988
1 vote

### Why is $\Phi\otimes \operatorname{Id}_n$ being positive on maximally entangled states sufficient to know that $\Phi$ is CP?

You can skip point 3 since $\Phi(X) = AXA^\dagger$ is a CP map and a sum of CP maps is again CP. The map $\Phi$ is CP because $(\Phi \otimes {\rm Id})(Z)= (A\otimes I)Z(A\otimes I)^\dagger$ – clearly ...
• 5,423

### Why does code switching not allow for universal fault-tolerant quantum computation?

One reference is here. The authors switch between the 7-qubit Steane code and 15-qubit Reed-Muller code. Clifford group operators can be performed in the Steane code, and the T-gate in the 15-qubit ...
• 21

### Qiskit library.gaussian() does not accept parametric expression

Just change library.gaussian to become library.Gaussian with capital G. Qiskit Pulse contains both ...
• 3,920
1 vote
Accepted

### Filtering operation is trace decreasing?

Yes. Generally you should think of filtering as being a measurement. You're only describing the effect of one measurement outcome. There's generally a second one such that the net effect is trace ...
• 46k
1 vote

### How to comparing a quantum channel with a unitary?

I found the following two works solving this problem. They selected several reference states and took the HS product between the final states evolved by the target unitary and the quantum channel. ...
• 121
Accepted

### Can any rank-$n$ POVM be realized as a rank-one POVM?

Is this an exercise? The answer is yes, you can do it, but I'm not going to tell you what the equivalent rank-1 POVM is. In general, any higher-rank POVM is equivalent to a rank-1 POVM if you relabel ...
• 1,593
### Can any rank-$n$ POVM be realized as a rank-one POVM?
You could define $$V_F^S u \equiv \sum_a |a\rangle\otimes (S^a\sqrt{F^a}\,u), \qquad u \in\mathcal X,$$ where $S^a$ is any unitary. Then $V_F^S$ is also an isometry and  F^a=(V_F^S)^\dagger (\...