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This paper addresses foundational challenges in defining error channels for higher-dimensional quantum systems by analyzing the non-equivalent formulations of the Pauli X gate. By extending bit-flip models to qudits, it clarifies how different definitions distinctly impact entanglement measures like Negativity across Werner states. This theoretical work is essential for refining noise modeling and fidelity benchmarks in future high-dimensional quantum computing architectures.
On the issues arising when defining an X gate for qudits: Extending the Bit-Flip channel to $d$-dimensional systems
arXiv:2501.11579v5 Announce Type: replace Abstract: Given the current interest in quantum information tasks involving higher-dimensional systems, we discuss some of the issues that appear when extending the bit-flip channel to qutrit systems. The difficulties arise from different interpretations of the Pauli X gate for qubits, leading to at least three nonequivalent formulations. We compare our results with the commonly used cyclic one-parameter trit flip channels and demonstrate that they are particular cases of those more general formulations we present here. We also extend these channels to higher-dimensional qudit systems, defining various dit flip channels. Finally, we study their impact on the Negativity, as an entanglement measure, of qubit-qutrit and 2-qutrit Werner states. In doing so, we show the distinctiveness of these versions, as they affect the states' entanglement in very distinct ways.
Abstract:Given the current interest in quantum information tasks involving higher-dimensional systems, we discuss some of the issues that appear when extending the bit-flip channel to qutrit systems. The difficulties arise from different interpretations of the Pauli X gate for qubits, leading to at least three nonequivalent formulations. We compare our results with the commonly used cyclic one-parameter trit flip channels and demonstrate that they are particular cases of those more general formulations we present here. We also extend these channels to higher-dimensional qudit systems, defining various dit flip channels. Finally, we study their impact on the Negativity, as an entanglement measure, of qubit-qutrit and 2-qutrit Werner states. In doing so, we show the distinctiveness of these versions, as they affect the states' entanglement in very distinct ways.
10 pages, 10 figures. Accepted in Phys. Lett. A
arXiv:2501.11579 [quant-ph]
(or arXiv:2501.11579v5 [quant-ph] for this version)
https://doi.org/10.1016/j.physleta.2026.132018 DOI(s) linking to related resources
Full text under the publisher's open licence · 150 words
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