Research On Particle Trajectories During Welcher Weg(WW) Measurement

Quantum mechanics, combining with information technology, developes as a new branch of learning called quantum information. The essential difference between the quantum and classical information is that the process of the classical information is based on the classical physics, and the storage, transmission as well as process of quantum information comply with the laws of quantum mechanics. The point of departure of studying the quantum information is to use quantum state to represent information. In experiment, usually the physical carrier of the qubit is any two-state quantum system. In the theoretical research of this article, we use the orthogonal polarization states of photons. Quantum information theory, while dependent, to some extent,also enriches the content of quantum theory itself. In the meanwhile, despite the contribution to a deeper understanding of quantum theory, quantum information may also promote the resolve of the basis problems of quantum theory. For example, so far, there are still lots of underlying concepts and problems puzzling physicists. One representative of these is the history of a quantum particle. Namely, other than a classical particle traveling between two points always having a single trajectory as the history, a quantum particle, yet, as Feynman discussed, takes every possible path through space from one point to another. Even though the fathers of quantum mechanics preached that we cannot talk about a quantum particle between measurements, there is an extensive discussion of Welcher Weg(“Which Way”) detectors in the context of“complementarity” and other fundamental aspects of quantum mechanics. This article makes analysis on the trajectory of a quantum particle, adopting the Two-State Vector Formalism(TSVF) to describe the weak trace left by the particle, according to a proposal [L. Vaidman, Phys.Rev. A 87,052104(2013)] that the quantum particle was in the overlap of the forward and backward evolving wave functions.In the first chapter of the paper, that is, the introduction, we describe the basic knowledge involved in the theoretical analysis, including the basic theory of quantum measurement, the foundation of weak measurement and direct measurement of the wave function. At the same time,we investigate the research status of the particle trajectories. In the part of direct measurement of wave function, we also describe that of mixed state wave function. In the second chapter, we introduce the main method used, that is to say, the TSVF, with the basic introduction, the principles and related current applications of it, at the same time. In the chapter 3, we introduce the WW measurement and describe the state of quantum particle in a complex interferometer with the method of TSVF. Also, we provide some related content of the delayed-choiceexperiment. In chapter 4, we analyze the WW measurement with polarization in the interferometer, verifying that the photon was where both forward- and backward-evolving wave functions do not vanish, in which the TSVF provides a simple and natural explanation of the weak trace of the quantum particle. The chapter 5 makes a summary of the overall content of the paper.