Limits to multipartite entanglement generation with bosons and fermions

Many-photon interference in linear-optics setups can be exploited to generate and detect multipartite entanglement. Without recurring to any inter-particle interaction, many entangled states have been created experimentally, and a panoply of theoretical schemes for the generation of various classes of entangled states is available. Here, we present a unifying framework that accommodates the present experiments and theoretical protocols for the creation of multiparticle entanglement via interference. A general representation of the states that can be created is provided for bosons and fermions, for any particle number, and for any dimensionality of the entangled degree of freedom. Using this framework, we derive an upper bound on the generalized Schmidt number of the states that can be generated, and we establish bounds on the dimensionality of the manifold of these states. We show that { at the expense of a smaller success probability { more states can be created with bosons than with fermions, and give an intuitive interpretation of the state representation and of the established bounds in terms of superimposed many-particle paths.

线性光学装置中的多光子干涉可被用于产生和探测多体纠缠。在不借助任何粒子间相互作用的情况下，许多纠缠态已在实验中被创造出来，并且有大量用于产生各类纠缠态的理论方案。在此，我们提出一个统一的框架，它适用于当前通过干涉产生多粒子纠缠的实验和理论协议。对于玻色子和费米子，对于任意粒子数以及纠缠自由度的任意维度，我们给出了可产生态的一般表示。利用这个框架，我们推导出了可产生态的广义施密特数的上界，并确定了这些态的流形维度的界限。我们表明，以较小的成功概率为代价，用玻色子比用费米子能产生更多的态，并且从叠加多粒子路径的角度对态表示和所确定的界限给出了直观的解释。