No instrument gives you an infinite precision in which to encode information with or decode it back out (though in quantum systems the result quantizes to one of N possible states depending on the system, so this is moot). The other option is an infinite amount of time to continuously encode information, but practically decoherence becomes the limiting factor.
I don't have a formal education in QP so this comes from my engineering perspective of working on quantum computers.
I don't have a formal education in QP so this comes from my engineering perspective of working on quantum computers.