Ok I'll bite. But, I'm not even going to get into all the absurdities of observing particles and the resulting consequences....I'm going to just talk straight numbers.
First task is to discover some method where we can encode any photon to reliably represent 1 value from a set of 2^256. It would be required to hold this state indefinitely , and recovery of the encoding would require an error rate much less than 1:2^256...otherwise you start to lose keys. I'm no quantum physicist, but I follow the field as much as I am able, and as far as I'm aware, there are no properties, super states, spin configuration, or anything else at present that would allow anywhere NEAR that number of identifiable encoded states to be represented by a photon or any particle.
Secondly, even if we DID manage to find some property, state, *add sci-fi here*....the simple fact is, there are not enough photons, let alone particles of any kind, in the ENTIRE universe to encode all of the private key combinations onto. It is generally agreed that there are 10^80 particles in the known universe, and somewhere in the region of 10^65 photons. Even if a considerably larger portion of photons were available say 10^66 (which is 10 times more), the number available is still a long way off from 2^256 (or 10^77 as rightly pointed out below by another member).
Such a long way in fact, that you could take all of the photons and other particles in our solar system (that's the Sun, planets, rocks, comets, dust) millions of times over, and that wouldn't even come close to covering the numbers gap between available photons and 2^256.
Thirdly...storage of all these particles......if you packed them all as tight as you could together, you'd still need a "hard drive" about the size of a galaxy. But don't get too happy about your new Unibyte drive, because good old gravity is still around and you'd end up with a mega-blackhole, which would collapse so violently you'd probably end up with a rip in space time, followed by a "Big Bang"
Finally, food for thought......a modern, top of the range Xeon powered server, just counting from 0 all the way to 2^256, would consume ALL the energy within the Sun before it completed its task.
EDITED: as I made an error in my post as pointed out