# Tagged Questions

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### 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 ...
I am interested in the existence of a set of vectors $\{ v_{ij} \}_{ij} \subseteq \mathbb{C}^N$ for $i \in \{1,\dots,N\}$, $j \in \{1,\dots,N+1\}$ such that $\left\vert v^*_{ij} v_{ij'} \right\vert = ... 2answers 215 views ### Existence of a projection operator onto a classical set of density matrices I have a Hilbert space of quantum density matrices written in the Glauber-Sudarshan P representation - ie. we have coherent states$|\alpha \rangle$and we write density matrices as$$\rho = \int ... 1answer 590 views ### Bounding the von Neumann entropy of a density matrix with the Hilbert-Schmidt norm Question Suppose I have a$D$-dimensional density matrix$\rho_0\rho_0^\dagger = \rho_0 \quad, \quad \mathrm{Tr} \rho_0 = 1 \quad, \quad \rho_0 > 0,$with a known spectrum$\{\lambda_i^0\}$... 1answer 482 views ### Can the von Neumann entropy of a positive, positive semi-definite, and unit-trace density matrix with equal on-diagonal terms be bounded by equalizing all off-diagonal elements to their highest/lowest value? Statement of problem Consider the density matrix$M = (m_{i,j})$in$d$-dimensions with all positive elements:$m_{i,j} > 0$. From physics, a density matrix is Hermitian, positive semi-definite, ... 3answers 863 views ### Is there a useful generalization of the Schmidt decomposition to the tensoring together of 3 or more vector spaces? I've rewritten the question in math notation, and I've left the old version in physics bra-ket notation here. Background A simple consequence of the singular value decomposition is that any vector ... 1answer 166 views ### Operator compression preserving lowest energy eigenspace. I have a large ($10^6$by$10^6$) sparse ($0.4$% nonzero) hermitian matrix$H$arising from the discretization of an elliptic PDE. I would like to approximate$H$with a smaller matrix$H'$in such a ... 1answer 457 views ### What is the entropy of a density matrix which is the sum of two unitarily equivalent projectors? Construction Suppose I have a density matrix$\rho$which is proportional to a projector$P$formed by tensoring together$N$small projectors$P^{(i)}$of rank 2:$P^{(i)} = |a\rangle_i\langle a| + ...
Landau and Streater proved that a set of Kraus operators, Ai, is extremal if and only if the set $\{A_{k}^{\dagger}A_{l}\}_{k,l \ldots N}$ are linearly independent. I have seen very convincing ...