Is the Heisenberg uncertainty relation really violated?

Abstract

It has been pointed out that for some types of measurement the Heisenberg uncertainty relation seems to be violated. In order to save the situation a new uncertainty relation was proposed by Ozawa. Here we introduce revised definitions of error and disturbance taking into account the gain associated with generalized measurement interactions. With these new definitions, the validity of the Heisenberg inequality is recovered for continuous linear measurement interactions. We also examine the changes in distribution functions caused by the general measurement interaction and clarify the physical meanings of infinitely large errors and disturbances.

Measurement schemes for the spin quadratures on an ensemble of atoms

“…The measurement of the spin state and state reconstruction to visualize its quantum nature in the form of the quasiprobability distribution are interesting objective in its own right [19]. On the other hand, the FR interaction corresponds to a unitary operation used in a classical model for an indirect measurements [20], and recently several models of quantum measurements have been proposed to demonstrate the relation between an indirect measurement and its back action [21,22,23].…”

“…Hence, the partial swapping together with the phase shifter enables us to perform the homodyne tomography to reconstruct the spin state. The two-pass interaction is referred to as the noiseless quadrature transducer [22] associated with the contractive state measurement [14,21,23]. If we fold this two-pass scheme exploiting the FMPS then we have a simpler scheme for the homodyne tomography of the spin state with one DL and two interactions with a counter propagation as in FIG.…”