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Persistence of quantum triality relations in open n-dimensional systems

Pratidhwani Swain1,2,*, Ramita Sarkar3,4,*,†, Sukanta K. Tripathy1, and Prasanta K. Panigrahi4,5

  • *These authors contributed equally to this work.
  • †Contact author: ramitasarkar11@gmail.com
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APS Open Sci. 1, 000006 – Published 29 April, 2026

DOI: https://doi.org/10.1103/r9rn-7rj4

Abstract

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-, three-, and n-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. We further extend the study to non-Markovian amplitude damping, where environmental memory effects lead to nonmonotonic evolution and revivals of coherence and entanglement. These results demonstrate that the complementarity relation remains preserved even in open quantum systems, highlighting its robustness against decoherence for both Markovian and non-Markovian open-system dynamics and providing a unified analytical understanding of noisy quantum interferometry in low-dimensional systems.

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APS Open Sci. 1, 000006– Published 29 April, 2026
Vol. 1
  • Received 25 November 2025
  • Accepted 20 March 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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