title: Operationally invariant measure of the distance between quantum states by complementary measurements.
abstract: We propose an operational measure of distance of two quantum states, which conversely tells us their closeness. This is defined as a sum of differences in partial knowledge over a complete set of mutually complementary measurements for the two states. It is shown that the measure is operationally invariant and it is equivalent to the Hilbert-Schmidt distance. The operational measure of distance provides a remarkable interpretation of the information distance between quantum states.
authors.affiliation: School of Mathematics and Physics, The Queen's University, Belfast BT7 1NN, Northern Ireland, UK. jlee@am.qub.ac.uk
authors.forename: Jinhyoung
authors.initials: J
authors.lastname: Lee
authors.forename: M S
authors.initials: MS
authors.lastname: Kim
authors.forename: Caslav
authors.initials: C
authors.lastname: Brukner