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A non-commuting measurement transfers, via the apparatus, information encodedin a system's state to the external "observer". Classical measurementsdetermine properties of physical objects. In the quantum realm, the very samenotion restricts the recording process to orthogonal states as only those aredistinguishable by measurements. Therefore, even a possibility to describephysical reality by means of non-hermitian operators should \emph{volensnolens} be excluded as their eigenstates are not orthogonal. Here, we show thatnon-hermitian operators with real spectrum can be treated within the standardframework of quantum mechanics. Furthermore, we propose a quantum canonicaltransformation that maps hermitian systems onto non-hermitian ones. Similar toclassical inertial forces this transformation is accompanied by an energeticcost pinning the system on the unitary path.

Repeatability of measurements: Equivalence of hermitian and non-hermitian observables