Uncertainty Principle from Operator Asymmetry

Xingze Qiu

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arXiv · 2509.06760

Uncertainty Principle from Operator Asymmetry

Xingze Qiu

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Abstract

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.

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Xingze Qiu. 2025-09-08. Uncertainty Principle from Operator Asymmetry. https://arxiv.org/abs/2509.06760

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