Its main focus is in extracting information from matter at the microscopic scale

i think an infinite amount of quantum information can be extracted from a finite amount of matter

this isn't surpising given constant size cryptographic proofs of programs of arbitrary length or like bls signature aggregation, infinite information:data compression ratios. e.g. an infinite amount of information can be stored in 100 KB

this sometimes relies on creating a piece of data necessary to verify the information. e.g. in bls all public keys must be known in order to verify

so an infinite amount of information can be stored in a finite amount of data, but only a finite amount of information can later be read (bounded by amount of matter/free energy in universe)

art is similar, an infinite amount of meaning can be embedded in a piece of art using references, but the observer must know the references being made in order to observe them. but references are themselves quantum information, observed or not

this parallels quantum information itself. An infinite amount of quantum information can exist, but only a finite amount exists in time by being observed by life before heat death