# Tag Info

Accepted

### Inverting the depolarizing channel

The existence of the inverse of a linear map is independent of the way the map affects the trace. Moreover, if an invertible map preserves a property then its inverse necessarily also preserves the ...
• 24.2k

### Why does the twirl of a quantum channel give a depolarizing channel?

I hope you do not mind if I zoom out a bit and talk about representation theory. I think a more general approach helps understanding the essential bits and will be helpful if you encounter similar ...
• 5,317
Accepted

### Why does the twirl of a quantum channel give a depolarizing channel?

Nielsen's paper cited in the question simplifies the arguments originally laid out in two papers by Horodecki family. This answer sketches the original arguments and is meant to complement the nice ...
• 24.2k
Accepted

### How can the depolarizing channel, defined as $\mathcal E(\rho) = (1-p)\rho + p\frac{I}{2}$, be a linear quantum operation?

The correct linear form of the depolarizing channel is $$\varepsilon(\rho) = (1-p)\rho + p\frac{I}{2}{\rm Tr}(\rho).$$ For density matrices ${\rm Tr}(\rho)=1$, so you can usually see the form ...
• 7,612
Accepted

### What is the adjoint of the depolarizing channel?

TL;DR: $\Phi^*=\Phi$. If quantum channel $\Psi:\mathcal{X}\to\mathcal{Y}$ has a Kraus representation $\Psi(X)=\sum_iK_iXK_i^\dagger$ then its adjoint $\Psi^*:\mathcal{Y}\to\mathcal{X}$ has a Kraus ...
• 24.2k
Accepted

### Decoding the Steane Code

The error correction protocol for any CSS code (such as the Steane code) is described in e.g. Section 10.4.2 of Nielsen & Chuang, although it's much easier to understand in the stabilizer picture. ...
• 316