8
votes
Accepted
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?
This answer won't actually give you a bound, but will provide some information that may help you in your search. You may be able to find an answer in the random matrix theory literature if you ...
- 4,568
5
votes
Accepted
Is the diamond norm subadditive under composition?
For arbitrary linear super-operators $U_j$ and $V_j\def\D{\mathrm{Diamond}} \def\Dn#1{\lVert #1 \rVert_\diamond}\def\le{\leqslant} $, we have
$$\def\D{\mathrm{Diamond}} \def\Dn#1{\lVert #1 \rVert_\...
- 11k
4
votes
Accepted
Bounding diamond norm distance using probability of error in transmission of classical information
Intuition
The expression $\|\mathcal{A} - \mathcal{I}\|_\diamond$ quantifies how close the channel $\mathcal{A}$ is to the identity channel $\mathcal{I}$ which is the channel that preserves quantum ...
- 14.4k
4
votes
Accepted
Diamond norm distance bound on Stinespring dilations of channels
Yes, in fact there exists Stinespring dilations such that
$$\frac{\|N_1-N_2\|_{cb}}{\sqrt{\|N_1\|_{cb}}+\sqrt{\|N_2\|_{cb}}}\leq \|V_1-V_2\|\leq \sqrt{\|N_1-N_2\|_{cb}}$$ where the distance between ...
- 1,577
4
votes
Is there a lower bound on the average diamond norm of two uniformly random unitaries U1 and U1 of dimension D that are sampled from haar measure?
The result you're looking for is effectively Proposition 19 of the paper: Almost all quantum channels are equidistant; which I'm rewriting here for convenience:
Let $U, V \in \mathcal{U}(d)$ be two ...
- 1,703
3
votes
Closeness of unitary dilations of CPTP maps
Let $V_i=U_i^\dagger(A\otimes I_K)U_i$ and $\sigma=\rho\otimes |0\rangle\langle0|$, then we have that $V_i$ is unitary and
$$\|\rho_1-\rho_2\|_1=\|tr_K\left((V_1\sigma V_1^\dagger -V_2\sigma V_2^\...
- 1,577
3
votes
Accepted
Choi matrix in QETLAB
QETLAB usually deals with channels as Choi operators. You can convert your Kraus operators to the Choi matrix by providing the Kraus operators as a cell array. Example with the amplitude damping ...
- 106
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