Physics – Quantum Physics
Scientific paper
2011-06-04
Physics
Quantum Physics
3 pages
Scientific paper
We motivate and prove a version of the birthday paradox for $k$ identical bosons in $n$ possible modes. If the bosons are in the uniform mixed state, also called the maximally mixed quantum state, then we need $k \sim \sqrt{n}$ bosons to expect two in the same state, which is smaller by a factor of $\sqrt{2}$ than in the case of distinguishable objects (boltzmannons). While the core result is elementary, we generalize the hypothesis and strengthen the conclusion in several ways. One side result is that boltzmannons with a randomly chosen multinomial distribution have the same birthday statistics as bosons. This last result is interesting as a quantum proof of a classical probability theorem; we also give a classical proof.
Arkhipov A. A.
Kuperberg Greg
No associations
LandOfFree
The bosonic birthday paradox does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The bosonic birthday paradox, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The bosonic birthday paradox will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-7417