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Residual error-disturbance uncertainties in successive spin-1/2 measurements tested in matter-wave optics

The indeterminacy inherent in quantum measurement is an outstanding character of quantum theory, which manifests itself typically in Heisenberg's error-disturbance uncertainty relation. In the last decade, Heisenberg's relation has been generalized to hold for completely general quantum measurements. Nevertheless, the strength of those relations has not been clarified yet for mixed quantum states. Recently, a new error-disturbance uncertainty relation (EDUR), stringent for generalized input states, has been introduced by one of the present authors. A neutron-optical experiment is carried out to investigate this new relation: it is tested whether error and disturbance of quantum measurements disappear or persist in mixing up the measured ensemble. Our results exhibit that measurement error and disturbance remain constant independent of the degree of mixture. The tightness of the new EDUR is confirmed, thereby validating the theoretical prediction.