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arXiv:2403.17171 · PRX Quantum

Generation of Genuine Multipartite Entangled States via Indistinguishability of Identical Particles

Kobra Mahdavipour, Farzam Nosrati, Stefania Sciara, Roberto Morandotti, Rosario Lo Franco

Published Dec 27, 2024• 7 citations

Abstract

Indistinguishability of identical particles is a resource for quantum information processing and has been utilized to generate entanglement from independent particles that spatially overlap only at the detection stage. Here, we introduce a controllable scheme capable of generating via three steps, i.e., initialization, deformation, and postselection, different classes of multipartite entangled states starting from a product state of N spatially distinguishable identical qubits. While our scheme is generalizable to any class of entangled bosonic and fermionic systems, we provide an explicit recipe for the generation of W , Dicke, GHZ, and cluster states, which are resource states for quantum information processing. Using graph-based representations within the framework of spatially localized operations and classical communication (sLOCC), we mathematically demonstrate a direct translation of the generation schemes of specific entangled states into colored, complex, and weighted digraphs, each corresponding to a given experimental setup. We also show that this graph-theoretical approach allows for the optimization of the generation efficiency of specific multipartite entangled states by exploring a variety of generation schemes. The presented theoretical approach, while already implementable with current linear optics architectures, has the potential to bring clear advantages over existing technologies, such as in quantum computing search algorithms and in the design of new experiments in quantum optics or other platforms. Published by the American Physical Society 2024

DOI: 10.1103/prxquantum.5.040350

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Quantum correlations between identical particles are at the heart of quantum technologies. Several studies with two identical particles have shown that the spatial overlap and indistinguishability between the particles are necessary for generating bipartite entanglement. On the other hand, researches on the extension to more than two-particle systems are limited by the practical difficulty to control multiple identical particles in laboratories. In this work, we propose schemes to generate two fundamental classes of genuine tripartite entanglement, i.e., GHZ and W classes, which are experimentally demonstrated using linear optics with three identical photons. We also show that the tripartite entanglement class decays from the genuine entanglement to the full separability as the particles become more distinguishable from each other. Our results support the prediction that particle indistinguishability is a fundamental element for entangling identical particles.

Identical quantum subsystems can possess a property which does not have any classical counterpart: indistinguishability. As a long-debated phenomenon, identical particles’ indistinguishability has been shown to be at the heart of various fundamental physical results. When concerned with the spatial degree of freedom, identical constituents can be made indistinguishable by overlapping their spatial wave functions via appropriately defined spatial deformations . By the laws of quantum mechanics, any measurement designed to resolve a quantity which depends on the spatial degree of freedom only and performed on the regions of overlap is not able to assign the measured outcome to one specific particle within the system. The result is an entangled state where the measured property is shared between the identical constituents. In this work, we present a coherent formalization of the concept of deformation in a general N -particle scenario, together with a suitable measure of the degree of indistinguishability. We highlight the basic differences with non-identical particles scenarios and discuss the inherent role of spatial deformations as entanglement activators within the spatially localized operations and classical communication operational framework. This article is part of the theme issue ‘Identity, individuality and indistinguishability in physics and mathematics’.

The indistinguishability of quantum particles is widely used as a resource for the generation of entanglement. Linear quantum networks (LQNs), in which identical particles linearly evolve to arrive at multimode detectors, exploit the indistinguishability to generate various multipartite entangled states by the proper control of transformation operators. However, it is challenging to devise a suitable LQN that carries a specific entangled state or compute the possible entangled state in a given LQN as the particle and mode number increase. This research presents a mapping process of arbitrary LQNs to graphs, which provides a powerful tool for analyzing and designing LQNs to generate multipartite entanglement. We also introduce the perfect matching diagram (PM diagram), which is a refined directed graph that includes all the essential information on the entanglement generation by an LQN. The PM diagram furnishes rigorous criteria for the entanglement of an LQN and solid guidelines for designing suitable LQNs for the genuine entanglement. Based on the structure of PM diagrams, we compose LQNs for fundamental N -partite genuinely entangled states.

Entanglement is a fundamental feature of quantum mechanics and a key resource for quantum information processing. Among multipartite entangled states, Dicke states

|D_n^k\rangle

are distinguished by their permutation symmetry, which provides robustness against particle loss and enables applications for quantum communication and computation. Although Dicke states have been realized in various platforms, most optical implementations rely on postselection, which destroys the state upon detection and prevents its further use. A heralded optical scheme is therefore highly desirable. Here, we present a linear-optical heralded scheme for generating arbitrary Dicke states

|D_n^k\rangle

with

3n+k

photons through the framework of the linear quantum graph (LQG) picture. By mapping the scheme design into the graph-finding problem, and exploiting the permutation symmetry of Dicke states, we overcome the structural complexity that has hindered previous approaches. Our results provide a resource-efficient pathway toward practical heralded preparation of Dicke states for quantum technologies.

Entanglement represents “the” key resource for several applications of quantum information processing, ranging from quantum communications to distributed quantum computing. Despite its fundamental importance, deterministic generation of maximally entangled qubits represents an on-going open problem. Here, we design a novel generation scheme exhibiting two attractive features, namely, i) deterministically generating different classes – namely, GHZ-like, W-like and graph states – of genuinely multipartite entangled states, ii) without requiring any direct interaction between the qubits. Indeed, the only necessary condition is the possibility of coherently controlling – according to the indefinite causal order framework – the causal order among the unitaries acting on the qubits. Through the paper, we analyze and derive the conditions on the unitaries for deterministic generation, and we provide examples for unitaries practical implementation. We conclude the paper by discussing the scalability of the proposed scheme to higher dimensional genuine multipartite entanglement (GME) states and by introducing some possible applications of the proposal for quantum networks.