Structure and Flow Observables in Complementarity Dynamics of Open Two-Qubit Systems

Abstract

Quantitative complementarity constrains how local predictability, fringe visibility, and bipartite concurrence share an information budget at a given instant, but an instantaneous balance does not by itself identify environmental memory. We therefore distinguish a structure diagnostic from two temporal flow diagnostics for open two-qubit dynamics. The structure distance \(\Delta _D\) measures the largest separation between the complementarity deficit and the global linear entropy along a trajectory. The concurrence-revival flow \(N_C\) accumulates positive concurrence increments, whereas the budget-recovery flow \(N_{-D}\) accumulates positive increments of the shifted complementarity budget. Local amplitude-damping and dephasing channels, a \(31\times 61\) parameter scan, comparisons with local Breuer–Laine–Piilo trace-distance-backflow proxies, an exact Bell-sector identity, and a general flow bound establish distinct diagnostic roles. The structure distance depends predominantly on state preparation, the concurrence flow selectively records entanglement revivals, and the budget flow responds more broadly and can remain nonzero without trace-distance backflow. The framework is therefore not a new non-Markovianity measure; it provides a reproducible way to separate state-space organization from temporal recovery in complementarity dynamics.