Uncertainty Principle from Operator Asymmetry
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908821485518848 |
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| author | Qiu, Xingze |
| author_facet | Qiu, Xingze |
| contents | The uncertainty principle is fundamentally rooted in the algebraic asymmetry between observables. We introduce a new class of uncertainty relations grounded in the resource theory of asymmetry, where incompatibility is quantified by an observable's intrinsic, state-independent capacity to break the symmetry associated with another. This ``operator asymmetry,'' formalized as the incompatibility norm, leads to a variance-based uncertainty relation for pure states that can be tighter than the standard Robertson bound. Most significantly, this framework resolves a long-standing open problem in quantum information theory: the formulation of a universally valid, product-form uncertainty relation for the Wigner-Yanase skew information. We demonstrate the practical power of our framework by deriving tighter quantum speed limits for the dynamics of nearly conserved quantities, which are crucial for understanding non-equilibrium phenomena such as prethermalization and many-body localization. This work provides both a new conceptual lens for understanding quantum uncertainty and a powerful, versatile toolkit for its application. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_06760 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Uncertainty Principle from Operator Asymmetry Qiu, Xingze Quantum Physics Quantum Gases Mathematical Physics The uncertainty principle is fundamentally rooted in the algebraic asymmetry between observables. We introduce a new class of uncertainty relations grounded in the resource theory of asymmetry, where incompatibility is quantified by an observable's intrinsic, state-independent capacity to break the symmetry associated with another. This ``operator asymmetry,'' formalized as the incompatibility norm, leads to a variance-based uncertainty relation for pure states that can be tighter than the standard Robertson bound. Most significantly, this framework resolves a long-standing open problem in quantum information theory: the formulation of a universally valid, product-form uncertainty relation for the Wigner-Yanase skew information. We demonstrate the practical power of our framework by deriving tighter quantum speed limits for the dynamics of nearly conserved quantities, which are crucial for understanding non-equilibrium phenomena such as prethermalization and many-body localization. This work provides both a new conceptual lens for understanding quantum uncertainty and a powerful, versatile toolkit for its application. |
| title | Uncertainty Principle from Operator Asymmetry |
| topic | Quantum Physics Quantum Gases Mathematical Physics |
| url | https://arxiv.org/abs/2509.06760 |