Photon encoding and computational limit of the universe The amount of information or entropy that can be contained in a region of space is given by the Bekenstein Bound: 
$I \leq \frac{2\pi RE} {hc \ln2}$
However, recent publications have shown information encoding in multiple dimensions, up to 10 dimensions on a single photon(Kues et al.)
What is the relationship between photon encoding in multiple dimensions and the Bekenstein Bound? And more broadly, the computational limitations of our universe?
 A: I think this link will be useful, particularly when he begins discussing the 5th argument. The answer as to why quantum computing doesn't violate the Bekenstein Bound is that if we have $n$ two dimensional entangled quantum systems, qubits, (the argument works similarly with 10 dimensional systems, except we work with a base of 10 instead of 2) there is a theorem, the Holevo Theorem which gives the amount of reliable classical bits that can be recovered from the system, namely $n$ classical bits. The system requires $2^n$ complex variables to describe, so given an $n$ sufficiently large, we could certainly make it look like we are violating the Bekenstein Bound, e.g. by having a system which requires $2^{10000}$ continuous complex variables to completely specify, but we couldn't "cash the system out". That is we couldn't recover even a minuscule fraction of that information from the system. Thus when we consider the number of classical bits stored in a quantum system, it still only scales linearly with the number of quantum bits, and thus we can't violate the Bekenstein Bound.
