J. Dressel, Y. Choi, A. N. Jordan
We theoretically investigate a generalized "which-path" measurement on an
electronic Mach-Zehnder Interferometer (MZI) implemented via Coulomb coupling
to a second electronic MZI acting as a detector. The use of contextual values,
or generalized eigenvalues, enables the precise construction of which-path
operator averages that are valid for any measurement strength from the
available drain currents. The form of the contextual values provides direct
physical insight about the measurement being performed, providing information
about the correlation strength between system and detector, the measurement
inefficiency, and the proper background removal. We find that the detector
interferometer must display maximal wave-like behavior to optimally measure the
particle-like which-path information in the system interferometer,
demonstrating wave-particle complementarity between the system and detector. We
also find that the degree of quantum erasure that can be achieved by
conditioning on a specific detector drain is directly related to the ambiguity
of the measurement. Finally, conditioning the which-path averages on a
particular system drain using the zero frequency cross-correlations produces
conditioned averages that can become anomalously large due to quantum
interference; the weak coupling limit of these conditioned averages can produce
both weak values and detector-dependent semi-weak values.
View original:
http://arxiv.org/abs/1105.2587
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