Persistence of Quantum Triality Relations in Open Qubit and Qutrit Systems

TL;DR

This work derives closed-form expressions for visibility $V^2$, predictability $P^2$, and entanglement $\varepsilon^2$ in two- and three-path interferometers, establishing a universal triality $V^2+P^2+\varepsilon^2=1$ in both pure and open-system settings. Using a system–path framework, it shows how these quantities evolve under amplitude damping and phase damping for qubits and qutrits, revealing that decoherence redistributes coherence, population imbalance, and system–environment correlations but preserves the overall sum. The results demonstrate the robustness of quantum complementarity against common noise models and provide a unified analytical understanding of noisy interferometry across low-dimensional Hilbert spaces, with implications for photonic and atomic implementations and potential extensions to higher dimensions and non-Markovian dynamics.

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- 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.

Figures (4)

• Figure 1: Two-slit interferometer with path detector states $|d_1\rangle$ and $|d_2\rangle$.
• Figure 2: Three-slit (qutrit) interferometer showing path--detector correlations $|d_1\rangle$, $|d_2\rangle$, and $|d_3\rangle$.
• Figure 3: (a) Qubit and (b) qutrit visibility, predictability, and entanglement under amplitude damping.
• Figure 4: (a) Qubit and (b) qutrit visibility, predictability, and entanglement under phase damping.