玻色生日悖论
The bosonic birthday paradox
摘要：
我们激发和证明了一个版本的生日悖论的$k$相同的玻色子在$n$可能的模式。如果玻色子处于均匀混合态，也称为最大混合量子态，那么我们需要$k \sim \sqrt{n}$玻色子来期待两个处于相同状态的玻色子，这比可区分物体（玻尔兹曼粒子）的情况小$\sqrt{2}$倍。虽然核心结果是基本的，我们推广的假设，并加强在几个方面的结论。一个附带的结果是，具有随机选择的多项分布的玻尔兹曼与玻色子具有相同的生日统计。这最后一个结果是有趣的量子证明的经典概率定理，我们也给一个经典的证明。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
