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Science

Characterization of Multipartite Entanglement for One Photon Shared Among Four Optical Modes

Scott B. Papp, Kyung Soo Choi, Hui Deng, Pavel Lougovski, S. J. van Enk, Harry J. Kimble

Published May 7, 2009• 125 citations
Publisher

Abstract

Access to genuine multipartite entanglement of quantum states enables advances in quantum information science and also contributes to the understanding of strongly correlated quantum systems. We report the detection and characterization of heralded entanglement in a multipartite quantum state composed of four spatially distinct optical modes that share one photon, a so-called W state. By randomizing the relative phase between bipartite components of the W state, we observed the transitions from four- to three- to two-mode entanglement with increasing phase noise. These observations are possible for our system because our entanglement verification protocol makes use of quantum uncertainty relations to detect the entangled states that span the Hilbert space of interest.

DOI
10.1126/science.1172260

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Access to genuine multipartite entanglement of quantum states enables advances in quantum information science and also contributes to the understanding of strongly correlated quantum systems. We report the detection and characterization of heralded entanglement in a multipartite quantum state composed of four spatially distinct optical modes that share one photon, a so-called W state. By randomizing the relative phase between bipartite components of the W state, we observed the transitions from four- to three- to two-mode entanglement with increasing phase noise. These observations are possible for our system because our entanglement verification protocol makes use of quantum uncertainty relations to detect the entangled states that span the Hilbert space of interest.
Multipartite entanglement is a key resource for quantum technologies, yet its certification typically relies on correlations from measurements involving all particles, making it increasingly vulnerable to imperfections as the system size grows. Here we report the first experimental demonstration of genuine multipartite entanglement detection from correlations with the minimum possible nontrivial support, known as the entanglement detection length (EDL). Using a photonic platform, we certify W, Dicke, and cluster states with entanglement witnesses constructed from correlations at the EDL. In particular, we verify genuine multipartite entanglement of three- and four-qubit W states and a four-qubit Dicke state using two-body correlations, and of a four-qubit cluster state using three-body correlations. For the four-photon Dicke state, we further show that this minimal-correlation strategy is more robust than the compared global witness under the analyzed local-basis-misalignment model. We also find that, within the witness families considered here, increasing the number of measured subsets enhances the tolerance to noise. These results establish entanglement detection at the EDL limit as a measurement-efficient route to multipartite entanglement certification.
Abstract Quantum entanglement is usually revealed via a well aligned, carefully chosen set of measurements. Yet, under a number of experimental conditions, for example in communication within multiparty quantum networks, noise along the channels or fluctuating orientations of reference frames may ruin the quality of the distributed states. Here, we show that even for strong fluctuations one can still gain detailed information about the state and its entanglement using random measurements. Correlations between all or subsets of the measurement outcomes and especially their distributions provide information about the entanglement structure of a state. We analytically derive an entanglement criterion for two-qubit states and provide strong numerical evidence for witnessing genuine multipartite entanglement of three and four qubits. Our methods take the purity of the states into account and are based on only the second moments of measured correlations. Extended features of this theory are demonstrated experimentally with four photonic qubits. As long as the rate of entanglement generation is sufficiently high compared to the speed of the fluctuations, this method overcomes any type and strength of localized unitary noise.
Characterizing entanglement of systems composed of multiple particles is a very complex problem that is attracting increasing attention across different disciplines related to quantum physics. The task becomes even more complex when the particles have many accessible levels, i.e., they are of high dimension, which leads to a potentially high-dimensional multipartite entangled state. These are important resources for an ever-increasing number of tasks, especially when a network of parties needs to share highly entangled states, e.g., for communicating more efficiently and securely. For these applications, as well as for purely theoretical arguments, it is important to be able to certify both the high-dimensional and the genuine multipartite nature of entangled states, possibly based on simple measurements. Here we derive a novel method that achieves this and improves over typical entanglement witnesses like the fidelity with respect to states of a Greenberger-Horne-Zeilinger (GHZ) form, without needing more complex measurements. We test our condition on paradigmatic classes of high-dimensional multipartite entangled states like imperfect GHZ states with random noise, as well as on purely randomly chosen ones and find that, in comparison with other available criteria our method provides a significant advantage and is often also simpler to evaluate.
Optical multi-mode systems provide large scale Hilbert spaces that can be accessed and controlled using single photon sources, linear optics and photon detection. Here, we consider the bipartite entanglement generated by coherently distributing M photons in M modes to two separate locations, where linear optics and photon detection is used to verify the non-classical correlations between the two M -mode systems. We show that the entangled state is symmetric under mode shift operations performed in the two systems and use this symmetry to derive correlations between photon number distributions detected after a discrete Fourier transform (DFT) of the modes. The experimentally observable correlations can be explained by a simple and intuitive rule that relates the sum of the output mode indices to the eigenvalue of the input state under the mode shift operation. Since the photon number operators after the DFT do not commute with the initial photon number operators, entanglement is necessary to achieve strong correlations in both the initial mode photon numbers and the photon numbers observed after the DFT. We can therefore derive entanglement witnesses based on the experimentally observable correlations in both photon number distributions, providing a practical criterion for the evaluation of large scale entanglement in optical multi-mode systems. Our method thus demonstrates how non-classical signatures in large scale optical quantum circuits can be accessed experimentally by choosing an appropriate combination of modes in which to detect the photon number distributions that characterize the quantum coherences of the state.