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arXiv:2404.08124 · Quantum Information Processing

Quantum correlations in general qubit–qudit axially symmetric states

Saeed Haddadi, E. I. Kuznetsova, Mikhail A. Yurischev

Published Apr 7, 2025• 4 citations
arXivHTMLPDF
DOI
10.1007/s11128-025-04719-4

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We investigate the quantum correlations in an axially symmetric hybrid qubit-qutrit system subjected to different noisy environments. We first introduce a physical model and analyze its Hamiltonian structure, emphasizing the role of hybrid dimensionality and axial symmetry. The effects of decoherence are then examined under two local noise mechanisms, namely dephasing and phase-flip channels, acting on the qubit and qutrit subsystems in both symmetric and asymmetric configurations. Quantum correlations are quantified using negativity to capture entanglement and quantum discord based on linear entropy to characterize more general nonclassical correlations. Our results show that both thermal fluctuations and phase noise lead to a monotonic degradation of quantum correlations, with increasing temperature accelerating coherence loss and inducing entanglement sudden death at finite temperatures. While negativity vanishes abruptly under sufficiently strong noise, quantum discord persists beyond the entanglement threshold, revealing residual quantum correlations in mixed states. We further demonstrate that asymmetric noise configurations significantly enhance the robustness of both entanglement and discord by partially shielding coherence in the less affected subsystem. A comparative analysis reveals that phase-flip noise is more destructive than pure dephasing, leading to faster suppression of quantum correlations.
Visualizing the d-valued quantum state-space of quantum systems serves as a foundational pillar for the scientific research and practical applications in quantum computing and information science, where d >= 2. The 2-valued quantum states of a qubit are elegantly visualized on the three-dimensional Bloch sphere. In contrast, expanding this geometrical paradigm to visualize higher d-valued quantum states of a qudit (d >= 3), e.g., a qutrit (d=3), ququadit (d=4), and quintit (d=5), leads to severe structural and topological complexities. This paper introduces a new generalized three-dimensional framework to effectively visualize higher d-valued quantum states of a qudit, in the aspects of ease of illustration, structural simplicity, and natural representation for researchers and engineers. We called this new framework the "multi-axial projective sphere (MAPS)", which consists of n projectional intersecting spatial axes, where 0 <= n <= d-1. We also propose a group of novel d-valued phase axial-based gates, to swivel and shift d-valued quantum states of a qudit along these n axes. Our generalized framework could be used for visualizing high-dimensional data for practical applications, e.g., machine learning, quantum machine learning, and quantum chemistry, where every axis of the MAPS represents a single feature of such data with its corresponding distinct values.