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arXiv:1610.00642 · Physical Review Letters

Entanglement by Path Identity

Mario Krenn, Armin Hochrainer, Mayukh Lahiri, Anton Zeilinger

Published Feb 23, 2017• 146 citations
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Abstract

Quantum entanglement is one of the most prominent features of quantum mechanics and forms the basis of quantum information technologies. Here we present a novel method for the creation of quantum entanglement in multipartite and high-dimensional systems. The two ingredients are (i) superposition of photon pairs with different origins and (ii) aligning photons such that their paths are identical. We explain the experimentally feasible creation of various classes of multiphoton entanglement encoded in polarization as well as in high-dimensional Hilbert spaces-starting only from nonentangled photon pairs. For two photons, arbitrary high-dimensional entanglement can be created. The idea of generating entanglement by path identity could also apply to quantum entities other than photons. We discovered the technique by analyzing the output of a computer algorithm. This shows that computer designed quantum experiments can be inspirations for new techniques.

DOI
10.1103/physrevlett.118.080401

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Quantum entanglement is one of the most prominent features of quantum mechanics and forms the basis of quantum information technologies. Here we present a novel method for the creation of quantum entanglement in multipartite and high-dimensional systems. The two ingredients are (i) superposition of photon pairs with different origins and (ii) aligning photons such that their paths are identical. We explain the experimentally feasible creation of various classes of multiphoton entanglement encoded in polarization as well as in high-dimensional Hilbert spaces-starting only from nonentangled photon pairs. For two photons, arbitrary high-dimensional entanglement can be created. The idea of generating entanglement by path identity could also apply to quantum entities other than photons. We discovered the technique by analyzing the output of a computer algorithm. This shows that computer designed quantum experiments can be inspirations for new techniques.
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The physics associated with multipartite high-dimensional entanglement is different from that of multipartite two-dimensional entanglement. Therefore, preparing multipartite high-dimensional entanglements with linear optics is challenging. This study proposes a preparation protocol of multiphoton GHZ state with arbitrary dimensions for optical systems. Auxiliary entanglements realize a high-dimensional entanglement gate to connect the high-dimensional entangled pairs to a multipartite high-dimensional GHZ state. Specifically, we use the path degrees of freedom of photons to prepare a four-partite, three-dimensional GHZ state. Our method can be extended to other degrees of freedom to generate arbitrary GHZ entanglements in any dimension.
Quantum entanglement plays an important role in quantum information processes, such as quantum computation and quantum communication. Experiments in laboratories are unquestionably crucial to increase our understanding of quantum systems and inspire new insights into future applications. However, there are no general recipes for the creation of arbitrary quantum states with many particles entangled in high dimensions. Here we exploit a recent connection between quantum experiments and graph theory and answer this question for a plethora of classes of entangled states. We find experimental setups for Greenberger-Horne-Zeilinger states, WWW states, general Dicke states, and asymmetrically high-dimensional multipartite entangled states. This result sheds light on the producibility of arbitrary quantum states using photonic technology with probabilistic pair sources and allows us to understand the underlying technological and fundamental properties of entanglement.
Abstract Quantum entanglement is one of the most important resources in quantum information. In recent years, the research of quantum entanglement mainly focused on the increase in the number of entangled qubits or the high-dimensional entanglement of two particles. Compared with qubit states, multipartite high-dimensional entangled states have beneficial properties and are powerful for constructing quantum networks. However, there are few studies on multipartite high-dimensional quantum entanglement due to the difficulty of creating such states. In this paper, we experimentally prepared a multipartite high-dimensional state ∣Ψ442⟩=12(∣000⟩+∣110⟩+∣221⟩+∣331⟩)\left|{\Psi }_{442}\right\rangle =\frac{1}{2}(\left|000\right\rangle +\left|110\right\rangle +\left|221\right\rangle +\left|331\right\rangle )∣Ψ442​⟩=21​(∣000⟩+∣110⟩+∣221⟩+∣331⟩) Ψ 442 = 1 2 ( 000 + 110 + 221 + 331 ) by using the path mode of photons. We obtain the fidelity F = 0.854 ± 0.007 of the quantum state, which proves a real multipartite high-dimensional entangled state. Finally, we use this quantum state to demonstrate a layered quantum network in principle. Our work highlights another route toward complex quantum networks.
We review recent theoretical and experimental works where are proposed and demonstrated how to use photon pairs created by spontaneous parametric down-conversion to generate entangled states of D-dimensional quantum systems, or qudits. This is the first demonstration of high-dimensional entanglement based on the intrinsic transverse momentum entanglement of the type-II down-converted photons. The qudit space is defined by an aperture made up of an opaque screen with D slits (paths), placed in the arms of the twin photons. By manipulating the pump beam profile we can prepare different entangled states of these possible paths. We focus our attention on an important case for applications in quantum information: the maximally entangled states. Experimental results for qudits with D=4 and D=8 are shown and measuring a two-photon conditional interference, we also demonstrate the nonclassical character of the correlations.
We introduce the concept of hypergraphs to describe quantum optical experiments with probabilistic multiphoton sources. Every hyperedge represents a correlated photon source, and every vertex stands for an optical output path. Such a general graph description provides new insights for producing complex high-dimensional multiphoton quantum entangled states, which go beyond limitations imposed by pair creation via spontaneous parametric down-conversion. Furthermore, the properties of hypergraphs can be investigated experimentally. For example, the NP-complete problem of deciding whether a hypergraph has a perfect matching can be answered by experimentally detecting multiphoton events in quantum experiments. By introducing complex weights in hypergraphs, we show a general many-particle quantum interference and manipulating entanglement in a pictorial way. Our work paves the path for the development of multiphoton high-dimensional state generation and might inspire new applications of quantum computations using hypergraph mappings.