New answers tagged information-theory
2
votes
Accepted
What are the antisymmetric terms in $\sigma_{mn}$ in the expression for the Fisher information?
Antisymmetric means that $\sigma_{nm}=-\sigma_{mn}$. Since the sum ranges over all values of $m$ and $n$, adding an antisymmetric term adds something proportional to
$$|\langle \psi_m^\lambda|\...
- 2,919
0
votes
How to show $T(\rho,\sigma)≥\sum_i|r_i − s_i|$ with $r_i,s_i$ eigenvalues of $\rho,\sigma$?
Here's a rephrasing of the same approach to the proof, using a slightly different notation.
You want to prove that
$$T(\rho,\sigma) \equiv \frac12\|\rho-\sigma\|_1 \ge \frac12\sum_k |\lambda_k(\rho) - ...
glS♦
- 21.7k
2
votes
Is it true that $|r_i-s_i| \le 1/2$ for all $i$, where $r_i$ and $s_i$ are the eigenvalues of density matrices $\rho$ and $\sigma$?
In this proof, we assume that the trace distance between $\rho$ and $\sigma$ is upper-bounded by $\frac{1}{\mathrm{e}}<\frac12$.
As mentioned by glS in the comments, the trace distance is lower-...
- 4,636
1
vote
What is the conditional min-entropy of a pure bipartite state?
Reading again the paper you linked, I think the way the authors were thinking about the result was of showing this via the relations between conditional min- and max-entropies, see discussion at the ...
glS♦
- 21.7k
3
votes
Accepted
What is the conditional min-entropy of a pure bipartite state?
I'll use an equivalent definition of the min-entropy
$$
\begin{aligned}
H_{\min}(A|B) = - \log_2 \min& \quad \lambda \\
\mathrm{s.t.}& \quad \rho_{AB} \leq \lambda I_A \otimes \sigma_B \\
&...
- 4,906
1
vote
What is the conditional min-entropy of a pure bipartite state?
Remember that the max relative entropy satisfies, in general,
$$D_{\rm max}(\rho\|\sigma) = \log \inf\{\eta\ge0:\,\, \rho\le \eta \sigma\}.$$
In particular,
$$D_{\rm max}(\rho\|I\otimes \sigma)=\log \...
glS♦
- 21.7k
2
votes
Clarification about inverses in sandwiched Renyi divergence
Firstly, the sandwiched divergence can be infinite even when $\rho$ and $\sigma$ are not orthogonal. For example, consider $\rho = \frac{|0\rangle \langle 0| + |1\rangle\langle 1|}{2}$ and $\sigma = |...
- 4,906
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