New answers tagged trace-distance
3
votes
Accepted
Does proximity of two bipartite states in a norm force high overlap between the elements of the Schmidt bases?
No.
Here is an example without small Schmidt coefficients.
To this end, consider
$$
\lvert\phi\rangle = a\lvert0\rangle\lvert0\rangle + b \lvert1\rangle\lvert1\rangle\ ,
$$
and
$$
\lvert\psi\rangle = ...
- 5,598
2
votes
Does proximity of two bipartite states in a norm force high overlap between the elements of the Schmidt bases?
TL;DR: No such relation exists, because the upper bound on the norm fails to impose any constraints whatsoever on the basis elements corresponding to very small Schmidt coefficients $\sqrt{p_i}$ and $\...
- 20k
1
vote
Is fidelity of mixed $\sigma$ and pure $|\psi\rangle$ equal to $\||\psi\rangle\langle\psi|\sigma\|_1$?
No, in general $\langle\psi|\sigma|\psi\rangle\ne\||\psi\rangle\langle\psi|\sigma\|_1$.
Singular value decomposition
Recall that if
\begin{equation}
A=\sum_i s_i|a_i\rangle\langle b_i|\tag1
\end{...
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