IIt is shown that a weak measurement of a quantum system produces a new state
of the quantum system which depends on the prior state, as well as the
(uncontrollable) measured position of the pointer variable of the weak
measurement apparatus. The result imposes a constraint on hidden-variable
theories which assign a different state to a quantum system than standard
quantum mechanics. The constraint means that a crypto-nonlocal hidden-variable
theory can be ruled out in a more direct way than previously.Comment: 10 pages, 2 figures. Substantially revised to concentrate on weak
measurement transformation of states and application to crypto-nonlocal
hidden-variable theor