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arXiv:1411.5399 · Physical Review A

Characterizing multipartite entanglement without shared reference frames

Claude Klöckl, Marcus Huber

Published Apr 29, 2015• 60 citations
arXivHTMLPDF

Abstract

Multipartite entanglement constitutes one of the key resources in quantum information processing. We exploit correlation tensor norms to develop a framework for its experimental detection without the need for shared frames of reference. By bounding these norms for partially separable states and states of limited dimension, we achieve an extensive characterization of entanglement in multipartite systems in an experimentally feasible way. Furthermore, we show that both bi- and multipartite dimensionality of entanglement can be revealed by our methods.

DOI
10.1103/physreva.91.042339

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Multipartite entanglement constitutes one of the key resources in quantum information processing. We exploit correlation tensor norms to develop a framework for its experimental detection without the need for shared frames of reference. By bounding these norms for partially separable states and states of limited dimension, we achieve an extensive characterization of entanglement in multipartite systems in an experimentally feasible way. Furthermore, we show that both bi- and multipartite dimensionality of entanglement can be revealed by our methods.
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The experimental detection of multipartite entanglement usually requires a number of appropriately chosen local quantum measurements that are aligned with respect to a previously shared common reference frame. The latter, however, can be a challenging prerequisite, e.g., for satellite-based photonic quantum communication, making the development of alternative detection strategies desirable. One possibility for avoiding the distribution of classical reference frames is to perform a number of local measurements with settings distributed uniformly at random. In this Letter, we follow such a treatment and show that an improved detection and characterization of multipartite entanglement is possible by combining statistical moments of different order. To do so, we make use of designs that are pseudorandom processes allowing us to link the present entanglement criteria to ordinary reference frame independent ones. The strengths of our methods are illustrated in various cases, starting with two qubits and followed by more involved multipartite scenarios.
We derive a framework for quantifying entanglement in multipartite and high dimensional systems using only correlations in two mutually unbiased bases. We furthermore develop such bounds in cases where the second basis is not characterized, thus enabling entanglement quantification with minimal assumptions. To demonstrate the experimental feasibility of the approach we develop an experimental proposal with state of the art cameras and optical lenses and show that these methods enable a reliable characterization of sources of entangled photons with minimal effort.
We present in detail a statistical approach for the reference-frame-independent detection and characterization of multipartite entanglement based on moments of randomly measured correlation functions. We start by discussing how the corresponding moments can be evaluated with designs, linking methods from group and entanglement theory. Then, we illustrate the strengths of the presented framework with a focus on the multipartite scenario. We discuss a condition for characterizing genuine multipartite entanglement for three qubits, and we prove criteria that allow for a discrimination of W -type entanglement for an arbitrary number of qubits.
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.
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.