Limits to multipartite entanglement generation with bosons and fermions

Abstract

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 the 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.

19 pages, 5 figures, Appendix A is a review of existing literature, with material from PRL 101, 010503 (2008) [arxiv:0806.1882] and PRL 102, 030502 (2009). Shortened introduction, version accepted by PRA

References in corpus (21)

• Entanglement detection
• Experimental entanglement of six photons in graph states
• Quantum Teleportation Between Distant Matter Qubits
• Entangling Independent Photons by Time Measurement
• Experimental entanglement of a six-photon symmetric Dicke state
• General criterion for the entanglement of two indistinguishable particles
• The maximally entangled symmetric state in terms of the geometric measure
• Experimental observation of an entire family of four-photon entangled states
• Entanglement of multiparty stabilizer, symmetric, and antisymmetric states
• Generation of Symmetric Dicke States of Remote Qubits with Linear Optics
• Measuring Qutrit-Qutrit Entanglement of Orbital Angular Momentum States of an Atomic Ensemble and a Photon
• Many-particle interference beyond many-boson and many-fermion statistics
• Four-Photon (In)Distinguishability Transition
• Entanglement of Indistinguishable Particles
• Preparation and characterization of arbitrary states of four-dimensional qudits based on biphotons
• Multi-qubit entanglement engineering via projective measurements
• Implementation of quantum operations on single photon qudits
• Optimal local expansion of W states using linear optics and Fock states
• Experimentally implementable criteria revealing substructures of genuine multipartite entanglement
• Projection of two biphoton qutrits onto a maximally entangled state
• Generation of Total Angular Momentum Eigenstates in Remote Qubits