Abstract
The Schmidt decomposition and the correlational analysis based on it make it possible to identify statistical dependences between various subsystems of a single physical system. The systems under consideration can be both quantum states and classical probability distributions. In this study, two different physical systems are considered: quantum Schrödinger cat states and double-slit interference of microparticles. It is shown that the considered systems have a single internal structure and can be described in general terms of interfering alternatives. An effective approach is developed that allows us to calculate optical characteristics of interference such as visibility and coherence. It is shown that the scalar product of the states of the environment of interfering alternatives acts as a natural generalization of the classical complex parameter of the coherence of light oscillations, which determines the visibility of the interference pattern. A simple quantitative relationship is obtained between the visibility of the interference pattern and the Schmidt number, which determines the level of connection between a quantum system and its environment. The developed approaches are generalized to the case of multidimensional Schrödinger cat states.
Highlights
The interference of quantum states is one of the cornerstones of the concept of quantum computing [1, 2]
It is important to note the interference effects that manifest themselves in quantum Schrödiger cat states, which are a superposition of coherent states [4] and are actively used in quantum optics [5,6,7]
Comparing the presented description of interfering quantum alternatives with the classical description of the phenomenon of coherence, we see that the scalar product of the states of the environment q2 = e1 e2 acts as a natural generalization of the classical complex parameter γ, called the degree of coherence of light oscillations [25]
Summary
The interference of quantum states is one of the cornerstones of the concept of quantum computing [1, 2]. Schrödinger’s cat states are of great interest in quantum communications and quantum optics and are used in various fields, such as quantum computing in continuous variables [8,9,10], quantum error correction codes [11, 12], and precision measurements [13, 14] These practical applications explain the rapid development of the theory of quantum correlations in bipartite quantum states. The proposed method is generalized to the case of multidimensional Schrödiger cat states In this generalization, analytical formulas are obtained that make it possible to model and calculate the arising interference patterns and characteristics. The results obtained can be used in the development of high-dimensional quantum information processing systems
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