A study on Heisenberg-Weyl linear maps

2025/06/05 by Saikat Patra, Patra, Saikat, Bihalan Bhattacharya +1
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic and Geometric Analysis #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Physics (quant-ph)

paper · pdf · doi:10.48550/arxiv.2506.05097

openalex publication_date 2025/06/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Heisenberg-Weyl operators provide a Hermitian generalization of Pauli operators in higher dimensions. Positive maps arising from Heisenberg-Weyl operators have been studied along with several algebraic and spectral properties of Heisenberg-Weyl observables. This allows to generalize the study of Pauli type maps in higher dimesional algebra of operators.

Citations

• A class of Schwarz qubit maps with diagonal unitary and orthogonal symmetries
• A class of entanglement witnesses and a realignment-like criterion
• Dynamical maps beyond Markovian regime
• The Theory of Quantum Information
• Positive linear maps of operator algebras
• Entanglement detection
• Quantum entanglement
• Separability Criterion for Density Matrices

Related

• Pauli operators and the d-bar-Neumann problem
• Weyl's Relations, Integrable Matrix Models and Quantum Computation
• Non Hermitian Operators with Real Spectrum in Quantum Mechanics
• A class of Schwarz qubit maps with diagonal unitary and orthogonal symmetries
• Torus as phase space: Weyl quantization, dequantization and Wigner\n formalism