Operationally Invariant Measure of the Distance between Quantum States by Complementary Measurements

Jinhyoung Lee, M. S. Kim, Caslav Brukner

Published 2003-03-18, updated 2003-09-26Version 2

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.