Yakir Aharonov, Eliahu Cohen, Avshalom C. Elitzur
Weak measurement is unique in that it enables measuring noncommuting operators as well as observing delicate states predicted by the Two-State-Vector-Formalism (TSVF). This method can be made more effective, applicable even for a single particle. For this purpose we first revisit the basic principles of quantum measurement with the aid of the Michelson interferometer. Weak measurement is then introduced in a lucid and intuitive minor by a specific choice of a reflecting mirror. We next consider a photon going back and forth inside this device, oscillating between a definite and a superposed state, while subjected to alternating strong and weak measurements. This cyclic process enables directly measuring both the photon's position ("which-path") and its momentum (interference), without disturbing either. An alternative account of this result, not invoking weak values, is thoroughly considered and shown to be inconsistent. Next a practical application is demonstrated, measuring the various transmission coefficients of a multiport beam-splitter with the aid of a single photon, yet leaving the photon superposed. This method is then generalized to measurement of the wave-function itself, performed again on a single particle.
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http://arxiv.org/abs/1207.0655
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