2025/04/29 by Gen Kimura, Kimura, Gen, Aina Mayumi +7 · 2 citations
Computer Science · Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Noncommutative and Quantum Gravity Theories #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #Statistical Mechanics (cond-mat.stat-mech)
paper · pdf · doi:10.48550/arxiv.2504.20404
openalex publication_date 2025/04/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
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 new noncommutativity-induced term. This term represents a previously overlooked quantum contribution and becomes more pronounced as the state becomes more mixed. Moreover, it is expressed as the expectation value of a positive observable, namely the squared modulus of the commutator, and therefore preserves the direct, experimentally accessible character of the Robertson--Schrödinger relation. For two-level quantum systems, our relation becomes an exact equality for any state and any pair of observables, thereby ensuring the tightness of the bound in the strongest possible sense. The relation also yields, as a corollary, a complete proof of a general uncertainty bound that had previously been supported only by numerical evidence.