# Number of bits to represent quantum uncertainty?

I've seen some semi-related questions here, but nothing pertaining to uncertainty.

It has occurred to me (but I’m betting to others long before) is that a quantum state must be represented by a limited amount of information (i.e. bits, because Physics can be reduced to information theory).

Looking specifically at the uncertainty principle, the product of the precisions of position and momentum (or energy and time) must be greater than or equal to some lower limit (Planck’s constant over 2). Imagine that you took a bit of precision away from position (reducing its certainty by a factor of two) and gave it to momentum (doubling its certainty), then you’d get the same maximum precision. If you took into account Planck temperature (https://en.wikipedia.org/wiki/Absolute_hot), it might be possible to postulate a total number bits that could represent these quantities.

Do we know enough about physics to postulate some number of bits to represent this information?

If there is a limit on bits, does this imply some limits on maximum quantities? (I.e. can't have energy above some limit.)

• Your question is not very clear. I am right in thinking that the gist of what you are asking is "Does the uncertainty principle allow us to specify the state of a particle with a finite amount of information"? Or are you asking about the relationship between the uncertainty principle and information more generally? – By Symmetry Aug 11 '16 at 14:05
• Isn't quantum mechanics a counterexample to what you're proposing? In QM one has both the uncertainty principle and a continuum of states, so the former can't be enough to preclude the latter. – WillO Aug 11 '16 at 14:13
• If I can figure out an answer to this, I would next ponder that when a quantum feature (e.g. spin) is uncertain, that means there are currently no bits assigned to represent the state. – Timothy Miller Aug 11 '16 at 14:20
• there is at least a relation between the uncertainty of a measure and the bits needed to represent the result. To reach a perfect measure, one needs an infinity of bits, while for an incredible one , only 1 or a few are useful. That's with bits but you can build other objects which introduce a decreasing meaning of new bits and let know how to optimize the whole knowledge ( as defined in the context ) in bits. – user46925 Aug 11 '16 at 15:34