  Quantum Schrodinger cat states are of great interest in quantum
communications and quantum optics. These states are used in various scientific
fields such as quantum computing, quantum error correction and high-precision
measurements. The analysis of the Schrodinger cat states coherence is an
important task for their complete practical application. Our developed approach
makes it possible to estimate the coherence of the quantum Schrodinger cat
state of arbitrary dimension, as well as to find the interference visibility of
the state - an important optical characteristic. The obtained simple
quantitative relationship between coherence and the Schmidt number, as well as
the developed approach of reducing the multidimensional quantum cat state to a
two-mode analog allow us to analyze macroscopic states formed by a large number
of modes. Several explicit formulas for the reduced states that arise after
measuring of some modes of the considered multimode system are obtained. The
research results have significant application and can be used in the
development of high-dimensional quantum information processing systems.
