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Optical coherence redistribution and complementarity closure in exact non-Markovian photonic feedback channels

Matthias Jakob

Published Jun 5, 2026• 0 citations

Abstract

Non-Markovian optical channels can redistribute interferometric visibility,which-path information, and entanglement in ways that are not captured byconcurrence dynamics alone. Motivated by cavity-QED, waveguide-feedback,and related photonic reservoir architectures, we study an exactly solvabletwo-qubit mini-reservoir model and interpret its reduced dynamics as an effectivelocal photonic feedback channel. For the reduced two-qubit state, predictabilityPk, visibility Vk, and concurrence C obey the mixed-state relationP2k (t)+V 2k (t)+C2(t) = Bk(t) ≤ 1, where Bk(t) is the locally accessible complementaritybudget. Within the Hilbert–Schmidt formulation of completecomplementarity, we show that the corresponding deficit is closed exactly byMk(t) ≡ 1 − Bk(t) = 2Cnlhs(t) − C2(t). The remainder therefore identifiesthe part of the nonlocal optical coherence sector that is not already encodedin concurrence. Exact trajectories for Bell, nonmaximally entangled parity,superposition-of-Bell, and Werner initial states reveal memory-inducedcollapse-and-revival structure in the accessible budget, in the visibility sectorwhen local coherence is present, and in the remainder itself. Comparisonswith one-sided discord and with the purity deficit show that Mk(t)is a distinct reduced-state diagnostic rather than a relabeling of entanglement,discord, or mixedness. Because all quantities are reconstructed fromthe same reduced two-qubit state, the framework is naturally compatible with interferometric and tomographic readout in memory-bearing quantumopticalplatforms.

DOI: 10.5281/zenodo.20553203

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