# Questions tagged [depolarizing-channel]

A model for noise in quantum systems such as a decohering qubit that has particularly nice symmetry properties. The depolarizing channel is a “worst-case scenario” channel. It assumes that we just completely lose the input qubit with some probability, i.e., it replaces the lost qubit with the maximally mixed state.

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

I would like to understand in detail why the twirl of a quantum channel gives depolarizing channel, which is the starting point of randomized benchmarking. To be self-contained, let me set up the ...
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### Inverting the depolarizing channel

I have a depolarizing channel acting on $2^n \times 2^n$ Hermitian matrices, defined as $$\tag{1} \mathcal{D}_p (X) = p X + (1-p) \frac{\text{Tr}(X)}{2^n} \mathbb{I}_{2^n}$$ where $\mathbb{I}_{d}$ is ...
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### Decoding the Steane Code

The $[[5,1,3]]$ code is a perfect code basically meaning that the weight-0 and weight-1 error spaces completely fill out the $32$-dimensional Hilbert space. On the other hand, the $[[7,1,3]]$ Steane ...
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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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### Two qubit state + Depolarizing channel = Bell diagonal state?

In multiple sources, e.g. RGK, KGR, it is stated (without proof) that if you take any two qubit state and send it through a depolarizing channel, the resulting state would be a Bell-diagonal state. ...
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