The post-selection operator current

Autor: John E. Gray, Stephen R. Addison
Rok vydání: 2018
Předmět:
Zdroj: Quantum Studies: Mathematics and Foundations. 5:399-412
ISSN: 2196-5617
2196-5609
Popis: In this paper, we develop the concept of the post-selection operator current and we use it to extend the methodology of quantum mechanics into related fields of science and engineering. We begin by reviewing some results from standard quantum mechanics. We then introduce the post-selection operator current and note that the concept of the operator current provides a common framework for connecting underlying concepts in classical signal theory and quantum mechanics. Next, we explore the geometry of post-selection making use of the Pancharatnam phase. We illustrate the usefulness of the method through a series of simple examples; at each stage we link the results of quantum mechanics to applications in signal processing. We then simplify some results by introducing a density operator. This simplification allows us to present a number of useful observations about weak values. We conclude by using the operator current explore the relationship between post-selection and gauge invariance. The methods developed in this paper enable us to characterize the time evolution of a post-selected operator. The methods can be applied to other evolutionary/transport equations including the Fokker–Planck equation, and the equation of Brownian motion.
Databáze: OpenAIRE
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