Complete positivity conditions for quantum qutrit channels

Abstract

We present an analysis of complete positivity (CP) constraints on qutrit quantum channels that have a form of affine transformations of generalized Bloch vector. For diagonal (damping) channels we derive conditions analogous to the ones that in qubit case produce tetrahedron structure in the channel parameter space.

Singular Value Decomposition and Matrix Reorderings in Quantum Information Theory

“…The detailed discussion of the CP conditions is presented in [4,18] for one-qubit quantum channels and in [25] for one-qutrit channels. …”

Spin Polarization-Scaling Quantum Maps and Channels

“…Quantum states of a spin-j particle are described by (2j + 1) × (2j + 1) density matrices ∈ S(H) satisfying the properties † = , tr[ ] = 1, and ϕ| |ϕ 0 for all |ϕ ∈ H, dimH = 2j + 1. Taking into account the normalization condition, the density matrix is defined by (2j + 1) 2 − 1 real parameters, which are usually treated as components of the generalized Bloch vector [1,2,10,19,28]. However, many physical phenomena can be explained and visualized via a spin polarization vector p ∈ R with components p i = tr[ J i ], where J 1 , J 2 , J 3 are usual (2j + 1)-dimensional representations of angular momentum operators (see, e.g., [34]).…”

Generalized three-party sharing of operations on remote single qutrit

“…This is the usually so-called degree-generalization issue. As a matter of fact, so far some researchers [9][10][11][12][13][14][15][16][17][18][19] have already considered the issue in ful¯lling some peculiar quantum tasks in some concrete quantum scenarios. Nonetheless, to our best knowledge, in QOS only Liu et al 7 have considered the simplest degree-generalization issue by far.…”