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Uncertainty Relation for Non-Hermitian Systems

Quantum Physics 2023-04-11 v3 Mathematical Physics math.MP

Abstract

We construct uncertainty relation for arbitrary finite dimensional PT invariant non-Hermitian quantum systems within a special inner product framework. This construction is led by good observables which are a more general class of operators. We show that the cumulative gain in the quantum Fisher information when measuring two good observables for such non-Hermitian systems is way better than their Hermitian counterpart. Minimum uncertainty states being the best candidates for this gain near the exceptional point supports the intelligent or simultaneous non-Hermitian quantum sensors.

Keywords

Cite

@article{arxiv.2206.02844,
  title  = {Uncertainty Relation for Non-Hermitian Systems},
  author = {Namrata Shukla and Ranjan Modak and Bhabani Prasad Mandal},
  journal= {arXiv preprint arXiv:2206.02844},
  year   = {2023}
}

Comments

9 pages, 5 figures

R2 v1 2026-06-24T11:41:02.352Z