  In general, classical measurement statistics of a quantum measurement is
disturbed by performing an additional incompatible quantum measurement
beforehand. Using this observation, we introduce a state-independent definition
of disturbance by relating it to the distinguishability problem between two
classical statistical distributions --- one resulting from a single quantum
measurement and the other from a succession of two quantum measurements.
Interestingly, we find an error-disturbance trade-off relation for any
measurements in two-dimensional Hilbert space and for measurements with
mutually unbiased bases in any finite-dimensional Hilbert space. This relation
shows that error should be reduced to zero in order to minimize the sum of
error and disturbance. We conjecture that a similar trade-off relation can be
generalized to any measurements in an arbitrary finite-dimensional Hilbert
space.
