Decomposable dynamics on matrix algebras

TL;DR

This paper investigates decomposable divisibility in quantum evolution families, providing conditions for symmetric qubit and qudit maps, and linking divisibility to positivity of generator coefficients, akin to CP-divisibility.

Contribution

It introduces necessary and sufficient conditions for D-divisibility in symmetric quantum maps and relates divisibility to positivity of time-dependent generator coefficients.

Findings

Conditions for D-divisibility in symmetric qubit and qudit maps

Reformulation of evolution generators in terms of positivity of coefficients

Analogy between D-divisibility and CP-divisibility via generator positivity

Abstract

We explore a notion of decomposably divisible (D-divisible) quantum evolution families, recently introduced in J. Phys. A: Math. Theor. 56, 485202 (2023). Both necessary and sufficient conditions are presented for highly-symmetric qubit and qudit dynamical maps. Through a restructurization of the evolution generators, we encode the decomposable divisibility into the positivity of time-dependent coefficients that multiply generators of D-divisible dynamical maps. This provides an analogy to the CP-divisibility property, which is equivalent to the positivity of decoherence rates that multiply Markovian semigroup generators.