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Questions tagged [diamond-norm]

In quantum information, the diamond norm is a distance metric between quantum operations. (Wikipedia)

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Bounding diamond norm distance using probability of error in transmission of classical information

Let us consider an encode, noisy channel and a decoder such that classical messages $m\in\mathcal{M}$ can be transmitted with some small error. That is, for a message $m$ that is sent by Alice, Bob ...
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1answer
81 views

Diamond norm distance bound on Stinespring dilations of channels

The diamond distance between two channels $\Phi_0$ and $\Phi_1$ is defined in this answer. $$ \| \Phi_0 - \Phi_1 \|_{\diamond} = \sup_{\rho} \: \| (\Phi_0 \otimes \operatorname{Id}_k)(\rho) - (\Phi_1 ...
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1answer
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Choi matrix in QETLAB

I am using QETLAB, a package for working with quantum information theory in Matlab and I have some doubts. I am trying to calculate diamond norms using such for some quantum channels. However, when ...
4
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2answers
250 views

Is there a lower bound on the average diamond norm of two uniformly random unitaries U1 and U1 of dimension D that are sampled from haar measure?

I could not find any lower bound on the diamond norm for two uniformly random unitaries of dimension D sampled from the haar measure.
6
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0answers
166 views

What are the "nice" properties of the diamond norm and why is it used?

I have heard about the diamond norm, and from what I understood it is a "nice" tool to quantify quality of quantum gates in the NISQ era. I would like to know a little more before going in detail in ...
6
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1answer
208 views

Is the diamond norm subadditive under composition?

The diamond norm distance between two operations is the maximum trace distance between their outputs for any input (including inputs entangled with qubits not being operated on). Is it the case that ...