Some Implications of the Aharonov Ansatz to Sensing

          @misc{ pirsa_PIRSA:16060075,
            doi = {10.48660/16060075},
            url = {https://pirsa.org/16060075},
            author = {Gray, John},
            keywords = {Quantum Foundations},
            language = {en},
            title = {Some Implications of the Aharonov Ansatz to Sensing},
            publisher = {Perimeter Institute},
            year = {2016},
            month = {jun},
            note = {PIRSA:16060075 see, \url{https://pirsa.org}}
          }
          

Abstract

There is a common framework for the measurement problem for sensors such as radars, sonars, and optics in a common language by casting analysis of signals in the language of quantum mechanics (Rigged Hilbert Space). The use of this language can reveal a more detailed understanding of the underlying interactions of a return signal that are not usually brought out by standard signal processing design techniques. The weak measurement Ansatz first provided by the Aharonov, Albert and Vaidman paper (A2V) that introduced weak values to the world provides an explicit means to consider all interactions of a signal with an object by using what we term the Aharonov Ansatz. The Aharonov Ansatz for sensing can summarized as: 1. Any sensor measurement process, whether active or passive can be thought of as determining the mathematical operator's characteristics of a signal's interaction with a object. 2. Certain types of interaction operators can be "post-selected" for in the return signal when the broadcast signal is known for either a single or multiple operators so receiver design can be optimized. 3. In principle detectors can design can be optimized, "matched" to signal interaction for these operators (operator matched filter), so mathematical solutions to receiver (in the classical sense) design or the design of apparatus of difficult to measure quantum interactions can be improved as has been reported in the literature. 4. Matching or post-selection to a given operator, when possible, maximizes ability to detect a "signal" or the characteristics of an interaction. Finally, in this talk we note a connection between this work and a the variational functional used in perturbation theory in quantum mechanics.