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International Journal of Theoretical Physics

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

Matthias Jakob

Published Sep 19, 2026• 0 citations
Publisher
DOI
10.1007/s10773-026-06486-z

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

Matthias Jakob

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.

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

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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

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Anthony Gandon, Samuele Piccinelli, Max Rossmannek +4 more

Simulating the dynamical properties of large-scale many-fermion systems is a longstanding goal of quantum chemistry, material science and condensed matter. Local fermion-to-qubit encodings have opened a new path for practical fermionic simulations on digital quantum hardware where fermionic statistics are not enforced at the hardware level. In this paper, we explore these local encodings from the perspective of the corresponding time-evolution unitaries. Specifically, we propose a new framework for digital implementations of these qubit-encoded fermionic time-evolution unitaries based on \emph{flow sets}, which are one-dimensional subsets of the directed fermionic interaction graph. We find that any local fermionic encoding, when restricted to a given flow set, adopts a simple structure that we can classify systematically. For each categorized flow-set form, we propose a low-depth qubit quantum circuit that implements the time evolution unitary using the stabilizer formalism. As an application of our construction, we introduce novel flow-based decompositions for known two-dimensional encodings, leading to efficient circuit decompositions of time-evolution unitaries. We generally observe a space-time trade-off, where mappings with larger qubit-to-fermion ratios yield shallower time-evolution quantum circuits.

quant-pharXiv:2512.11418•Dec 15, 2025•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
Simulating the dynamical properties of large-scale many-fermion systems is a longstanding goal of quantum chemistry, material science and condensed matter. Local fermion-to-qubit encodings have opened a new path for practical fermionic simulations on digital quantum hardware where fermionic statistics are not enforced at the hardware level. In this paper, we explore these local encodings from the perspective of the corresponding time-evolution unitaries. Specifically, we propose a new framework for digital implementations of these qubit-encoded fermionic time-evolution unitaries based on \emph{flow sets}, which are one-dimensional subsets of the directed fermionic interaction graph. We find that any local fermionic encoding, when restricted to a given flow set, adopts a simple structure that we can classify systematically. For each categorized flow-set form, we propose a low-depth qubit quantum circuit that implements the time evolution unitary using the stabilizer formalism. As an application of our construction, we introduce novel flow-based decompositions for known two-dimensional encodings, leading to efficient circuit decompositions of time-evolution unitaries. We generally observe a space-time trade-off, where mappings with larger qubit-to-fermion ratios yield shallower time-evolution quantum circuits.