Uncertainty Principle from Operator Asymmetry

• URL: http://arxiv.org/abs/2509.06760v1
• Date: Mon, 08 Sep 2025 14:50:32 GMT
• Title: Uncertainty Principle from Operator Asymmetry
• Authors: Xingze Qiu,
• Abstract summary: We introduce a new class of uncertainty relations grounded in the resource theory of asymmetry.<n>This framework resolves a long-standing open problem in quantum information theory.<n>We demonstrate the practical power of our framework by deriving tighter quantum speed limits for the dynamics of nearly conserved quantities.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 asymmetry norm, leads to a variance-based uncertainty relation for pure states that can be tighter than the standard Robertson bound, especially in the near-compatible regime. 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 toolkit for its application.

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