Search arXiv⌕ Search

arXiv · math/0102138

Lattice structures for quantum channels

Abstract

We suggest that a certain one-to-one parametrization of completely positive maps on the matrix algebra might be useful in the study of quantum channels. This is illustrated in the case of binary quantum channels. While the algorithm is quite intricate, it admits a simple, lattice structure representation.

Explore related subjects

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

T. Constantinescu. 2001-03-20. Lattice structures for quantum channels. https://arxiv.org/abs/math/0102138

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

Pointwise convergence of noncommutative discrete spherical ergodic averages

In this paper, we establish spherical maximal inequalities associated with commuting trace-preserving automorphisms on von Neumann algebras, extending Magyar-Stein-Wainger's discrete spherical maximal inequalities to the noncommutative setting. On a noncommutative probability space, we further prove that, under a strong ergodicity assumption, the corresponding discrete spherical averages converge bilaterally almost uniformly to $τ(x)1$ for every $x\in L_p(\mathcal M)$, $\frac{d}{d-2}<p\leq\infty$, when $d\geq5$.

math.OA↗

Values of Rokhlin Dimension for Integer Actions

For an action of the integers on a C*-algebra, we show that the only possible values for the Rokhlin dimension (with commuting towers) are $0,1,2$ and $+\infty$. We study these values for certain classes of C*-algebras, and show that there is an automorphism of the Jiang--Su algebra with the property that its Rokhlin dimension with and without commuting towers are distinct.

math.OA↗

Algebras, Kernels and Correspondences

This is a nearly complete draft of our paper in which we attempt to do three things. First, we show that when formulated in the context of reproducing kernel correspondences over Rieffel's category, Normod-$M$, the Kolmogorov decomposition/representation theorem of Ball, Marx, and Vinnikov is functorial in $M$. Second, we investigate relations between our work and the work of Clouâtre and Hartz concerning multipliers of reproducing kernels. This investigation leads to interesting questions about the geometry of the matricial unit disc associated with a correspondence over $M$. And third, we describe how some of the recent work of Salomon, Shalit and Shamovich may be formulated in our setting. This leads to the notion of subvarieties, their quotients, and their relation with the structure of reproducing correspondences.

math.OA↗