We show that skew information introduced by Wigner and Yanase, which is a natural informational extension of variance for pure states, can be interpreted as a measure of quantum uncertainty. By virtue of skew information, we establish a new uncertainty relation in the spirit of Schrödinger, which incorporates both incompatibility (encoded in the commutator) and correlations (encoded in a new correlation measure related to skew information) between observables, and moreover is stronger than the conventional ones.
Editor’s remark: A counterexample to Theorem 1 has been found by K. Yanagi, S. Furuichi, and K. Kuriyama [IEEE Trans. Inf. Theory 51, No. 12, 4401–4404 (2005; Zbl 1171.94330)], as noted in the erratum of the present paper [ibid. 51, No. 12, 4432 (2005)].