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We propose a protocol for a controlled experiment to measure a weak value of the electron's spin in a solid state device [1]. The weak value, introduced by Aharonov et al. [2], is obtained by a two step procedure - weak measurement followed by a strong one (post-selection), where the outcome of the first measurement is kept provided a second post-selected outcome occurs.
The observation of weak values in a solid state device can open an intriguing window on fundamental aspects of quantum measurement including the access to simultaneous measurement of non-commuting observables, correlation between measurements, negative (pseudo-) probabilities.
The set-up we propose consists of a double quantum dot and a weakly coupled quantum point contact to be used as a detector. Anomalously large values of the spin of a two electron system are predicted, as well as negative values of the total spin. We also show how to incorporate the adverse effect of decoherence into this procedure. [1] Alessandro Romito, Yuval Gefen and Yaroslav M. Blanter, arXiv:0707.3695. [2] Y. Aharonov, D. Z. Albert, and L. Vaidman, Phys. Rev. Lett. 60, 1351 (1988). |
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