Complementarity balance in a solvable non-Markovian two-qubit model

We present a conservative reformulation of the complementarity analysis contained
in the underlying manuscript materials. The claim is restricted to the part that is
directly supported by the available derivations: an exact reduced-state balance for local
predictability, local visibility, and entanglement in an exactly solvable mini-reservoir model
for non-Markovian two-qubit dynamics. For each local qubit, the reduced budget is defined
as Bk(t) = P2
k (t) + V 2
k (t) + C2(t) and is completed by a remainder Mk(t) = 1 − Bk(t).
Within the Hilbert–Schmidt bookkeeping adopted from the source material, this remainder
is written as the nonlocal contribution beyond concurrence, Mk(t) = 2Cnl
hs(t)− C2(t). The
result is model bound and should not be read as a universal conservation law for arbitrary
combinations of coherence, discord, and entanglement measures. Instead, it isolates a precise
complementarity identity inside a controlled Markov-embedded open-system setting.