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arXiv:2203.14322 · Physical Review A

Generation and detection of discrete-variable multipartite entanglement with multirail encoding in linear-optics networks

Jun-Yi Wu

Published Sep 30, 2022• 2 citations
arXivHTMLPDF

Abstract

A linear-optics network is a multimode interferometer system, where indistinguishable photon inputs can create nonclassical interference that cannot be simulated with classical computers. Such nonclassical interference implies the existence of entanglement among its subsystems if we divide its modes into different parties. Entanglement in such systems is naturally encoded in multirail (multimode) quantum registers. For bipartite entanglement, a generation and detection scheme with multirail encoding was theoretically proposed [Wu and Hofmann, New J. Phys. 19, 103032 (2017)] and experimentally realized [Kiyohara et al., Optica 7, 1517 (2020)]. In this paper, we will take a step further to establish a theory for the detection of multirail-encoded discrete-variable genuine multipartite entanglement (GME) in fixed local-photon-number subspaces of linear-optics networks. We also propose a scheme for GME generation with both discrete-variable (single photons) and continuous-variable (squeezed states) light sources. This scheme allows us to reveal the discrete-variable GME in continuous-variable systems. The effect of photon losses is also numerically analyzed for the generation scheme based on continuous-variable inputs.

DOI
10.1103/physreva.106.032437

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A linear-optics network is a multimode interferometer system, where indistinguishable photon inputs can create nonclassical interference that cannot be simulated with classical computers. Such nonclassical interference implies the existence of entanglement among its subsystems if we divide its modes into different parties. Entanglement in such systems is naturally encoded in multirail (multimode) quantum registers. For bipartite entanglement, a generation and detection scheme with multirail encoding was theoretically proposed [Wu and Hofmann, New J. Phys. 19, 103032 (2017)] and experimentally realized [Kiyohara et al., Optica 7, 1517 (2020)]. In this paper, we will take a step further to establish a theory for the detection of multirail-encoded discrete-variable genuine multipartite entanglement (GME) in fixed local-photon-number subspaces of linear-optics networks. We also propose a scheme for GME generation with both discrete-variable (single photons) and continuous-variable (squeezed states) light sources. This scheme allows us to reveal the discrete-variable GME in continuous-variable systems. The effect of photon losses is also numerically analyzed for the generation scheme based on continuous-variable inputs.
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Single photon sources can be used to generate and control highly non-classical states of light. Here, we consider the possibility of generating bi-partite entanglement between two separate multi-photon states by splitting the input modes of the single photon sources into a mode distributed to AAA and a mode distributed to BBB. If multiple photons are combined at AAA and at BBB, the large variety of photon patterns observed after linear optics transformations of the local multi-mode systems can be used to characterize the non-classical correlation of this entangled state. However, the transformation between different photon number states in linear optics is a complicated problem, and further analysis is needed to understand the possible applications of this scalable quantum system. To obtain maximal complementarity between two measurements, we consider the unbiased interference of all input modes represented by a discrete Fourier transform of the multi-mode field. We identify characteristic patterns that can be used to identify non-classical correlations between the two multi-photon systems at AAA and BBB and derive a quantitative criterion for entanglement verification. Our results indicate that the large scale quantum operations can be achieved by a comparatively simple quantum network interfering the outputs of multiple single photons, where the size of the system mainly depends on the number of available single photon sources.
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First, we show how the quantum circuits for generating and measuring multi-party entanglement of qubits can be translated to continuous quantum variables. We derive sufficient inseparability criteria for NNN-party continuous-variable states and discuss their applicability. Then, we consider a family of multipartite entangled states (multi-party multi-mode states with one mode per party) described by continuous quantum variables and analyze their properties. These states can be efficiently generated using squeezed light and linear optics.