Etymologically, "quantum" is the neuter singular form of the Latin word meaning "how much." As used in English in physics, it's a noun. It refers to one indivisible unit, e.g., the photon is the quantum of light, and e is the quantum of electric charge. The plural is "quanta," which is the neuter plural form, used in English as a plural noun.
In phrases like "quantum mechanics," "quantum state," and "quantum information," it's a noun being used to modify a noun, like "elephant gun" or "sandwich shop." The antonym is "classical." (Sometimes people use "classical" in contradistinction to "relativistic" as well, but that's incorrect. Special relativity and general relativity are classical theories.)
Although phrases like "quantum mechanics" are completely set in stone by tradition, there are alternatives such as "quantal" and "quantum mechanical." E.g., people do often write "quantum mechanical behavior" rather than "quantum behavior." "Quantum theory" refers to the abstract theoretical framework (e.g., it states that wavefunctions are complex numbers), while "quantum mechanical theory" implies the nonclassical version of a particular theory, e.g., the liquid drop model of the nucleus is classical, but there is also a quantum mechanical theory of nuclear physics.