Persistence of Quantum Triality Relations in Open Qubit and Qutrit Systems

TL;DR

This paper investigates how the fundamental quantum relations among coherence, predictability, and entanglement persist in open qubit and qutrit systems under noise, revealing their robustness and providing analytical insights into noisy quantum interferometry.

Contribution

It derives analytical expressions for quantum properties in noisy conditions and demonstrates the persistence of triality relations in open quantum systems.

Findings

Amplitude damping redistributes coherence and population imbalance.

Phase damping reduces coherence but preserves predictability.

Quantum triality relations remain valid despite decoherence.

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.