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Physical Review A

Detecting multipartite spatial entanglement with modular variables

Mariana R. Barros, O. Jiménez Farías, Arne Keller, T. Coudreau, P. Milman, Stephen Patrick Walborn

Published Aug 5, 2015• 10 citations

Abstract

Interference phenomena of quantum systems have been studied in the context of fundamental aspects of quantum physics and are considered a necessary resource for quantum information. Here we investigate the interference of multiparticle wave packets in terms of modular variables, which is a natural and convenient way to describe two or more interfering wave functions. Through the modular-variable description, interesting phenomena appear such as the complementarity between the number of wave packets and the width of the peaks of the momentum distribution. In the multipartite case, this effect produces quantum entanglement. We derive entanglement criteria that test for bipartite entanglement in generic bipartitions of a multipartite quantum state and use these criteria to test for genuine $D$-partite entanglement.

DOI: 10.1103/physreva.92.022308

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Interference phenomena of quantum systems have been studied in the context of fundamental aspects of quantum physics and are considered a necessary resource for quantum information. Here we investigate the interference of multiparticle wave packets in terms of modular variables, which is a natural and convenient way to describe two or more interfering wave functions. Through the modular-variable description, interesting phenomena appear such as the complementarity between the number of wave packets and the width of the peaks of the momentum distribution. In the multipartite case, this effect produces quantum entanglement. We derive entanglement criteria that test for bipartite entanglement in generic bipartitions of a multipartite quantum state and use these criteria to test for genuine

D

-partite entanglement.

Complex forms of quantum entanglement can arise in two qualitatively different ways: either between many qubits or between two particles with higher-than-qubit dimension. While both the many-qubit frontier and the high-dimension frontier are well established, state-of-the-art quantum technology is becoming increasingly able to create and manipulate entangled states that simultaneously feature many particles and high dimension. Here, we investigate generic states that can be considered both genuinely high-dimensional and genuine multiparticle entangled. We consider a natural quantity that characterizes this key property. To detect it, we develop three different classes of criteria. These enable us both to probe the ultimate noise tolerance of this form of entanglement and to make detection schemes using sparse or even minimal measurement resources. The approach provides a simple way of benchmarking entanglement dimensionality in the multiparticle regime and general, platform-independent, detection methods that readily apply to experimental use.

Entanglement is deemed a valuable resource for quantum computing and lies at the heart of quantum information. At the same time, current experiments are venturing into the realm of quantum systems consisting of many particles. In this book, different aspects of entanglement and non-locality in multiparticle systems are investigated. First, it presents an approach for an experimental verification of non-locality and entanglement with a high statistical significance. Second, a criterion for genuine multiparticle entanglement is introduced. Furthermore, this criterion also allows for a way of quantifying multiparticle entanglement. Analytical criteria for entanglement in a special class of quantum states, so-called graph states, are presented. These criteria turn out to be also necessary for entanglement in certain cases. Finally, ways of generalizing a non-local hidden-variable model proposed by Leggett are shown.

We study the genuine multipartite entanglement of arbitrary n-partite quantum states by representing the density matrices in terms of the generalized Pauli operators. We introduce a general framework for detecting genuine multipartite entanglement and non full-separability of multipartite quantum states with arbitrary dimensions based on correlation tensors. Effective criterion is derived to verify the genuine multipartite entanglement. Detailed examples are given to show that the criterion detects more genuine multipartite entanglement than the existing criteria.

The problems of genuine multipartite entanglement detection and classification are challenging. We show that a multipartite quantum state is genuine multipartite entangled if the multipartite concurrence is larger than certain quantities given by the number and the dimension of the subsystems. This result also provides a classification of various genuine multipartite entanglements. We present a lower bound of the multipartite concurrence in terms of bipartite concurrences. While various operational approaches are available for providing lower bounds of bipartite concurrences, our results give an effective operational way to detect and classify genuine multipartite entanglement. As applications, genuine multipartite entanglement of tripartite systems is analyzed in detail.