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Results tagged with linear-algebra
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user 49887
Questions about the properties of vector spaces and linear transformations, including linear systems in general.
24
votes
0
answers
1k
views
conjectures regarding a new Renyi information quantity
In a recent paper http://arxiv.org/abs/1403.6102, we defined a quantity that we called the "Renyi conditional mutual information" and investigated several of its properties. We have some open conjectu …
- 483
4
votes
1
answer
295
views
variation of the Lieb concavity theorem
A special case of the well known Lieb concavity theorem states that the following function is concave on positive operators A and B:
$$
(A,B) \to \text{Tr} \{A^s X B^{1-s} X^\dagger \}
$$
for $s \in …
- 483
2
votes
1
answer
104
views
tensor stability of block-positive matrices
Let $X_{AB}$ be an operator acting on the tensor-product Hilbert space $\mathcal{H}_A \otimes \mathcal{H}_B$. Suppose that $X_{AB}$ is block positive, meaning that (in Dirac notation)
$\langle \psi | …
- 483
2
votes
tensor stability of block-positive matrices
The answer to this question is "no," there is a simple counterexample.
First, Fact 1: consider that a map $\mathcal{N}_{A\to B}$ is positive iff its Choi operator $J^{\mathcal{N}}_{AB}$ is block posi …
- 483