2026-11-11 東北大学
図1．新しく見出された不確定性関係。従来のロバートソン・シュレーディンガーの不確定性関係に、これまで捉えられていなかった非可換性に由来する新たな寄与が加わった。
＜関連情報＞
- https://www.tohoku.ac.jp/japanese/2026/11/press20261111-03-noncommutative.html
- https://www.nature.com/articles/s41534-026-01374-0
ロバートソン・シュレーディンガーを超えて：隠された非可換トレードオフを明らかにする一般的な不確定性関係 Beyond Robertson–Schrödinger: a general uncertainty relation unveiling hidden noncommutative trade-offs
Gen Kimura, Aina Mayumi, Hiromichi Ohno, Jaeha Lee & Dariusz Chruściński
npj Quantum Information Published:21 September 2026
DOI:https://doi.org/10.1038/s41534-026-01374-0 Early provide
Abstract
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.
