  The well studied quantum optical Schr\"{o}dinger cat state is a superposition
of two distinguishable states, with quantum coherence between these
macroscopically distinguishable states being of foundational and, in the
context of quantum-information processing, practical use. We refer to these
quantum-optical cat states as quantum dichotomous states, reflecting that the
state is a superposition of two options, and we introduce the term quantum
multichotomous state to refer to a superposition of multiple macroscopically
distinguishable options. For a single degree of freedom, such as position, we
construct the quantum multichotomous states as a superposition of Gaussian
states on the position line in phase space. Using this nomenclature, a quantum
tetrachotomous state (QTS) is a coherent superposition of four macroscopically
distinguishable states. We define, analyze and show how to create such states,
and our focus on the QTS is due to their exhibition of much richer phenomena
than for the quantum dichotomous states with lessons to going to general
multichotomous states with the quantum comb state as a limiting case. Our
characterization of the QTS involves the Wigner function, its marginal
distributions, and the photon-number distribution, and we discuss the QTS's
approximate realization in a multiple coupled-well system.
