Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

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

Matthias Jakob

Published Jun 5, 2026• 0 citations
Publisher

Abstract

We study complementarity dynamics in open two-qubit systems through the local budgetBA = P2A+ V 2A + C2 and its deficit DA = 1 − BA. The purpose is not to define a newnon-Markovianity measure, but to distinguish two diagnostic roles. Structure observablesdescribe how predictability, visibility, concurrence, and deficit are arranged along a statespacetrajectory, whereas flow observables record temporal recovery. Amplitude-damping anddephasing prototypes, finite parameter scans, BLP-like comparisons, and two analyticallysolvable Bell-sector results show that ΔD is mainly structural, while NC and N−D respond torevival windows. The framework therefore clarifies what complementarity budgets certify inopen two-qubit dynamics.

DOI
10.5281/zenodo.20552815

Related papers

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

Matthias Jakob

Abstract We develop a complementarity-based description of open two-qubit dynamics built aroundthe budget Bk(t) = P2k(t)+V 2k(t)+C2(t) and the associated deficit Dk(t) = 1−Bk(t). The mainoutcome is not a new universal witness of non-Markovianity, but a more useful split betweenstructure observables and flow observables. Using explicit prototype amplitude-damping anddephasing channels, together with asymmetric couplings and mixed initial states, we showthat deficit-based distances such as ∆D = maxt|Dk(t) − SL(t)| mainly encode state- andchannel-dependent geometry, whereas positive-variation functionals such as NC and N−Drespond more directly to memory-driven recovery. In addition, for an exactly solvable Bell-statedephasing sector we prove that the revival windows of C and −DA coincide and obtain closedexpressions for BA and DA. The paper reframes complementarity dynamics as a two-levelproblem: geometry of resource partition on one side and temporal backflow on the other. Theframework is tied to a same-dataset BLP-like benchmark and to two analytical propositionsthat anchor the relation between concurrence revival and deficit flow in solvable sectors and ongeneral revival intervals

•May 19, 2026•0 citations

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

Matthias Jakob

We present a conservative reformulation of the complementarity analysis containedin the underlying manuscript materials. The claim is restricted to the part that isdirectly supported by the available derivations: an exact reduced-state balance for localpredictability, local visibility, and entanglement in an exactly solvable mini-reservoir modelfor non-Markovian two-qubit dynamics. For each local qubit, the reduced budget is definedas Bk(t) = P2k (t) + V 2k (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 remainderis written as the nonlocal contribution beyond concurrence, Mk(t) = 2Cnlhs(t)− C2(t). Theresult is model bound and should not be read as a universal conservation law for arbitrarycombinations of coherence, discord, and entanglement measures. Instead, it isolates a precisecomplementarity identity inside a controlled Markov-embedded open-system setting.

•Jun 5, 2026•0 citations

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

Matthias Jakob

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.

•Jun 5, 2026•0 citations

Persistence of Quantum Triality Relations in Open Qubit and Qutrit Systems

Pratidhwani Swain, Ramita Sarkar, Sukanta K. Tripathy +1 more

We examine the complementarity among coherence (visibility), predictability, and entanglement for qubit and qutrit systems subjected to noisy quantum channels. Using the system-path entanglement framework, analytical expressions for all three quantities are derived for two- and three-slit interferometric setups. The study first establishes the validity of the triality relation in ideal conditions and then investigates its behavior under amplitude and phase damping. We find that amplitude damping redistributes coherence and population imbalance without violating complementarity, while phase damping reduces coherence but leaves predictability unchanged. These results demonstrate that the complementarity relation remains preserved even in open quantum systems, highlighting its robustness against decoherence and providing a unified analytical understanding of noisy quantum interferometry in low-dimensional systems.

quant-pharXiv:2511.23399•APS Open Science•Dec 1, 2025•2 citations

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

Matthias Jakob

International Journal of Theoretical Physics•Sep 19, 2026•0 citations

Holonomy and Complementarity in Open Quantum Systems

Eric R Bittner

Complementarity relations constrain the distribution of coherence, predictability, and openness in quantum systems. Here we show that, in open quantum systems, these local constraints acquire a geometric interpretation through quasistatic transport. For a driven dissipative qubit, the complementarity variables define cylindrical coordinates on the Bloch sphere, while openness appears geometrically as a radial deficit associated with reduction from a larger Hilbert space. Quasistatic driving induces a work connection on the resulting steady-state manifold whose curvature determines the cyclic response. Hamiltonian-aligned dissipation produces an exact work connection and vanishing cyclic work, whereas fixed pointer-basis dissipation generates non-integrable transport, finite curvature, and holonomic response. The resulting curvature admits a phase-resolved representation on the triality manifold and develops perturbatively with pointer--Hamiltonian mismatch. In the weak-mismatch limit, the curvature is governed by a competition between coherence-preserving and pure-dephasing channels, producing symmetry-related positive- and negative-curvature sectors. These results establish a direct connection between complementarity, dissipation, and geometric thermodynamic response, and show that cyclic quasistatic work provides an operational probe of nonequilibrium quantum geometry.

quant-pharXiv:2605.10800•May 12, 2026•0 citations
We study complementarity dynamics in open two-qubit systems through the local budgetBA = P2A+ V 2A + C2 and its deficit DA = 1 − BA. The purpose is not to define a newnon-Markovianity measure, but to distinguish two diagnostic roles. Structure observablesdescribe how predictability, visibility, concurrence, and deficit are arranged along a statespacetrajectory, whereas flow observables record temporal recovery. Amplitude-damping anddephasing prototypes, finite parameter scans, BLP-like comparisons, and two analyticallysolvable Bell-sector results show that ΔD is mainly structural, while NC and N−D respond torevival windows. The framework therefore clarifies what complementarity budgets certify inopen two-qubit dynamics.
Abstract We develop a complementarity-based description of open two-qubit dynamics built aroundthe budget Bk(t) = P2k(t)+V 2k(t)+C2(t) and the associated deficit Dk(t) = 1−Bk(t). The mainoutcome is not a new universal witness of non-Markovianity, but a more useful split betweenstructure observables and flow observables. Using explicit prototype amplitude-damping anddephasing channels, together with asymmetric couplings and mixed initial states, we showthat deficit-based distances such as ∆D = maxt|Dk(t) − SL(t)| mainly encode state- andchannel-dependent geometry, whereas positive-variation functionals such as NC and N−Drespond more directly to memory-driven recovery. In addition, for an exactly solvable Bell-statedephasing sector we prove that the revival windows of C and −DA coincide and obtain closedexpressions for BA and DA. The paper reframes complementarity dynamics as a two-levelproblem: geometry of resource partition on one side and temporal backflow on the other. Theframework is tied to a same-dataset BLP-like benchmark and to two analytical propositionsthat anchor the relation between concurrence revival and deficit flow in solvable sectors and ongeneral revival intervals
We present a conservative reformulation of the complementarity analysis containedin the underlying manuscript materials. The claim is restricted to the part that isdirectly supported by the available derivations: an exact reduced-state balance for localpredictability, local visibility, and entanglement in an exactly solvable mini-reservoir modelfor non-Markovian two-qubit dynamics. For each local qubit, the reduced budget is definedas Bk(t) = P2k (t) + V 2k (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 remainderis written as the nonlocal contribution beyond concurrence, Mk(t) = 2Cnlhs(t)− C2(t). Theresult is model bound and should not be read as a universal conservation law for arbitrarycombinations of coherence, discord, and entanglement measures. Instead, it isolates a precisecomplementarity identity inside a controlled Markov-embedded open-system setting.
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.
We examine the complementarity among coherence (visibility), predictability, and entanglement for qubit and qutrit systems subjected to noisy quantum channels. Using the system-path entanglement framework, analytical expressions for all three quantities are derived for two- and three-slit interferometric setups. The study first establishes the validity of the triality relation in ideal conditions and then investigates its behavior under amplitude and phase damping. We find that amplitude damping redistributes coherence and population imbalance without violating complementarity, while phase damping reduces coherence but leaves predictability unchanged. These results demonstrate that the complementarity relation remains preserved even in open quantum systems, highlighting its robustness against decoherence and providing a unified analytical understanding of noisy quantum interferometry in low-dimensional systems.
Complementarity relations constrain the distribution of coherence, predictability, and openness in quantum systems. Here we show that, in open quantum systems, these local constraints acquire a geometric interpretation through quasistatic transport. For a driven dissipative qubit, the complementarity variables define cylindrical coordinates on the Bloch sphere, while openness appears geometrically as a radial deficit associated with reduction from a larger Hilbert space. Quasistatic driving induces a work connection on the resulting steady-state manifold whose curvature determines the cyclic response. Hamiltonian-aligned dissipation produces an exact work connection and vanishing cyclic work, whereas fixed pointer-basis dissipation generates non-integrable transport, finite curvature, and holonomic response. The resulting curvature admits a phase-resolved representation on the triality manifold and develops perturbatively with pointer--Hamiltonian mismatch. In the weak-mismatch limit, the curvature is governed by a competition between coherence-preserving and pure-dephasing channels, producing symmetry-related positive- and negative-curvature sectors. These results establish a direct connection between complementarity, dissipation, and geometric thermodynamic response, and show that cyclic quasistatic work provides an operational probe of nonequilibrium quantum geometry.