Lunkes Christian, Brukner Caslav, Vedral Vlatko
QOLS, Blackett Laboratory, Imperial College London, London SW7 2BZ, England, UK.
Phys Rev Lett. 2005 Jul 15;95(3):030503. doi: 10.1103/PhysRevLett.95.030503. Epub 2005 Jul 13.
We investigate multipartite entanglement in a noninteracting fermion gas, as a function of fermion separation, starting from the many particle fermion density matrix. We prove that all multiparticle entanglement can be built only out of two-fermion entanglement. Although from the Pauli exclusion principle we would always expect entanglement to decrease with fermion distance, we surprisingly find the opposite effect for certain fermion configurations. The von Neumann entropy is found to be proportional to the volume for a large number of particles even when they are arbitrarily close to each other. We will illustrate our results using different configurations of two, three, and four fermions at zero temperature although all our results can be applied to any temperature and any number of particles.
我们从多粒子费米子密度矩阵出发，研究了非相互作用费米子气体中的多体纠缠，它是费米子间距的函数。我们证明，所有多体纠缠都只能由两体费米子纠缠构建而成。尽管从泡利不相容原理我们通常预期纠缠会随着费米子间距的增加而减小，但令人惊讶的是，我们发现对于某些费米子构型会出现相反的效应。即使大量粒子彼此任意靠近，冯·诺依曼熵也被发现与体积成正比。我们将通过零温下两个、三个和四个费米子的不同构型来说明我们的结果，不过我们所有的结果都可应用于任何温度和任何数量的粒子。
