Sufficient conditions for uniqueness of the weak value
J. Phys. A: Math. Theor. 45, 015304 (2012)
We review and clarify the sufficient conditions for uniquely defining the generalized weak value as the weak limit of... more We review and clarify the sufficient conditions for uniquely defining the generalized weak value as the weak limit of a conditioned average using the contextual values formalism introduced in Dressel, Agarwal and Jordan (2010 Phys. Rev. Lett. http://dx.doi.org/10.1103/PhysRevLett.104.240401). We also respond to criticism of our work by Parrott (arXiv:1105.4188v1) concerning a proposed counter-example to the uniqueness of the definition of the generalized weak value. The counter-example does not satisfy our prescription in the case of an underspecified measurement context. We show that when the contextual values formalism is properly applied to this example, a natural interpretation of the measurement emerges and the unique definition in the weak limit holds. We also prove a theorem regarding the uniqueness of the definition under our sufficient conditions for the general case. Finally, a second proposed counter-example by Parrott (arXiv:1105.4188v6) is shown not to satisfy the sufficiency conditions for the provided theorem.
Measuring which-path information with coupled electronic Mach-Zehnder interferometers
Phys. Rev. B 85, 045320 (2012).
We theoretically investigate a generalized “which-path” measurement on an electronic Mach-Zehnder Interferometer (MZI)... more 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 wavelike 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 and detector-dependent semiweak values.
Experimental Violation of Two-Party Leggett-Garg Inequalities with Semiweak Measurements
Phys. Rev. Lett. 106, 040402 (2011)
We generalize the derivation of Leggett-Garg inequalities to systematically treat a larger class of experimental... more We generalize the derivation of Leggett-Garg inequalities to systematically treat a larger class of experimental situations by allowing multi-particle correlations, invasive detection, and ambiguous detector results. Furthermore, we show how many such inequalities may be tested simultaneously with a single setup. As a proof of principle, we violate several such two-particle inequalities with data obtained from a polarization-entangled biphoton state and a semi-weak polarization measurement based on Fresnel reflection. We also point out a non- trivial connection between specific two-party Leggett-Garg inequality violations and convex sums of strange weak values.
12 views
Seen by:Contextual Values of Observables in Quantum Measurements
Phys. Rev. Lett. 104, 240401 (2010)
We introduce contextual values as a generalization of the eigenvalues of an observable that takes into account both... more We introduce contextual values as a generalization of the eigenvalues of an observable that takes into account both the system observable and a general measurement procedure. This technique leads to a natural definition of a general conditioned average that converges uniquely to the quantum weak value in the minimal disturbance limit. As such, we address the controversy in the literature regarding the theoretical consistency of the quantum weak value by providing a more general theoretical framework and giving several examples of how that framework relates to existing experimental and theoretical results.
35 views
Seen by: and 1 more
