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arXiv:quant-ph/9504011 · Reports on Mathematical Physics

The N-representability problem, the pseudo-spectral decomposition of antisymmetric 1-body operators, and collective behaviour

Hubert Grudziński

Published Apr 1, 1996• 1 citation
arXivHTMLPDF
DOI
10.1016/0034-4877(96)89765-5

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This paper develops a comprehensive framework for quantum information theory within the paradigm of pseudo-Hermitian quantum mechanics. We establish necessary and sufficient conditions for the existence of biorthogonal Riesz bases, a fundamental component in the formulation of pseudo-Hermitian quantum information. Additionally, we propose a spectral theorem for pseudo-Hermitian operators and explore their decomposition. We introduce key postulates of pseudo-Hermitian quantum mechanics and independently derive the time-evolution operator for pseudo-Hermitian systems. Furthermore, we extend the classical notion of quantum channels to pseudo-Hermitian quantum information theory and provide various characterizations, including the Kraus, Stinespring, and Choi representations. Our findings contribute to the mathematical foundations of non-Hermitian quantum mechanics and its applications in quantum information processing.