4 papers
Uncertainty Relation for a Single Observable
Haruki Yamashita, Aina Mayumi, Gen Kimura
Uncertainty relations are usually formulated as trade-off relations between two or more observables. Here we show that the uncertainty of a single observable already has a nontrivi…
Tight Generalization of Robertson-Type Uncertainty Relations
Gen Kimura, Aina Mayumi, Haruki Yamashita
We establish the tightest possible Robertson-type preparation uncertainty relation, which explicitly depends on the eigenvalues of the quantum state. The conventional constant $ \t…
Beyond Robertson-Schrödinger: A General Uncertainty Relation Unveiling Hidden Noncommutative Trade-offs
Gen Kimura, Aina Mayumi, Hiromichi Ohno +2
We report a universal improvement to the standard Robertson--Schrödinger uncertainty relation. Our result shows that the Robertson--Schrödinger lower bound can be supplemented by a…
Uncertainty relations based on state-dependent norm of commutator
Aina Mayumi, Gen Kimura, Hiromichi Ohno +1
We introduce two uncertainty relations based on the state-dependent norm of commutators, utilizing generalizations of the Böttcher-Wenzel inequality. The first relation is mathemat…