Entanglement is nowadays considered as a key quantity for the understanding of correlations, transport properties, and phase transitions in composite quantum systems, and thus receives interest beyond the engineered applications in the focus of quantum information science. We review recent experimental and theoretical progress in the study of quantum correlations under that wider perspective, with an emphasis on rigorous definitions of the entanglement of identical particles, and on entanglement studies in atoms and molecules.

Boson sampling holds the potential to experimentally falsify the extended Church-Turing thesis. The computational hardness of boson sampling, however, complicates the certification that an experimental device yields correct results in the regime in which it outmatches classical computers. To certify a boson sampler, one needs to verify quantum predictions and rule out models that yield these predictions without true many-boson interference. We show that a semiclassical model for many-boson propagation reproduces coarse-grained observables that are proposed as witnesses of boson sampling. A test based on Fourier matrices is demonstrated to falsify physically plausible alternatives to coherent many-boson propagation.

Identical particles exhibit correlations even in the absence of inter-particle interaction, due to the exchange (anti)symmetry of the manyparticle wavefunction. Two fermions obey the Pauli principle and anti-bunch, whereas two bosons favor bunched, doubly occupied states. Here, we show that the collective interference of three or more particles leads to much more diverse behavior than expected from the boson-fermion dichotomy known from quantum statistical mechanics. The emerging complexity of many-particle interference is tamed by a simple law for the strict suppression of events in the Bell multiport beam splitter. The law shows that counting events are governed by widely species-independent interference, such that bosons and fermions can even exhibit identical interference signatures, while their statistical character remains subordinate. Recent progress in the preparation of tailored many-particle

The Hong-Ou-Mandel effect is generalized to a configuration of n bosons prepared in the n input ports of a Bell multiport beam splitter. We derive a strict suppression law for most possible output events, consistent with a generic bosonic behavior after suitable coarse graining.PACS numbers: 03.67. Lx, 05.30.Jp, The Hong-Ou-Mandel (HOM) effect [1] is an impressive manifestation of the bosonic quantum nature of photons. In the original experiment, two identical photons are sent simultaneously (within their coherence time) through the two input ports of a balanced beam splitter. Since no interaction between the photons takes place, one would intuitively expect the photons to propagate independently and not presume any correlations in the number of photons measured at both output ports. Surprisingly, the photons always leave the setup together, but never exit at different ports. Such coincident events at both output ports are completely suppressed.This effect is used in many applications: The visibility of the dip in the coincident detection rate provides a characterization for the indistinguishability of two photons [2,3], and therewith for the quality of photon sources. HOM setups are used to project photons onto the maximally entangled |Ψ − Bell-state, and consequently to, both, create and detect such states [4]. This is used for example in entanglement swapping protocols [5] and quantum metrology [6]. Furthermore, the nondeterministic gate operations in linear optics quantum computation [7] are based on the HOM effect.It is suggestive to generalize the HOM setup for more than two photons and more than two input or output ports. Indeed, the enhancement of events with all particles in one port -bunching events -has been observed experimentally when several photons enter each of the two modes of an unbiased (i.e., balanced) two-port beam splitter [8,9]. For a specially designed biased setup of three particles and three input ports, the suppression of coincident events was shown [10]. In the case of a Bell multiport beam splitter [11,12] which redistributes n incoming particles to n ports in an unbiased way, it is known that coincident events are suppressed when n is even [13].All these results imply important applications, from the creation and detection of multipartite quditentangled states [14,15], over the implementation of entanglement swapping protocols for many particles and the design of efficient quantum gates for qudits [16], to the experimentally controlled transition from indistinguishability to distinguishability for many identical particles [17]. However, we still lack a comprehensive understanding of the n-particle, n-port generalization of the HOM effect, since the complexity of such a scattering problem scales very unfavorably with n: The number of interfering amplitudes as well as that of possible output events grow faster than exponentially. Hence, a detailed analysis of individual output events is prohibitive, and needs to be substituted by statistical considerations. This is the purpose of the ...