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OSA Advanced Photonics Congress

Multipartite d-Level Two-Photon Cluster States and Their Entanglement Detection Via Feasible Witness Operators

Stefania Sciara, Christian Reimer, Piotr Roztocki, David Moss, Lucia Caspani, William J. Munro, Michael Kues, Roberto Morandotti

Published Jan 1, 2020• 0 citations
Publisher

Abstract

We demonstrate the first multipartite d-level cluster state by using two-photon hyper-entanglement in time and frequency, and validate its genuine entanglement via a novel witness operator enabling feasible detection of any complex quantum state.
DOI
10.1364/iprsn.2020.iw1a.5

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Entanglement is an essential resource in quantum information science [1] and its presence in any quantum system can be experimentally detected through entanglement witness operators [2]. In particular, measuring a negative expectation value of a witness with high statistical confidence provides a necessary and sufficient condition to confirm the generation of a genuine multipartite [3] and/or d-level entangled state [4]. In recent years, the experimental generation of complex quantum states has intensified the need for witnesses that are capable of detecting such systems and are experimentally optimal at the same time. This means that the witness should require the least measurement effort (in terms of number and complexity of the measurement settings), include only projections on single qudits, while at the same time possessing a high noise tolerance (Fig. 1a). However, "experimentally-friendly" witnesses capable of accomplishing these tasks have not been derived yet.
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Certifying entanglement of a multipartite state is generally considered a demanding task. Since an N qubit state is parametrized by 4^{N}-1 real numbers, one might naively expect that the measurement effort of generic entanglement detection also scales exponentially with N. Here, we introduce a general scheme to construct efficient witnesses requiring a constant number of measurements independent of the number of qubits for states like, e.g., Greenberger-Horne-Zeilinger states, cluster states, and Dicke states. For four qubits, we apply this novel method to experimental realizations of the aforementioned states and prove genuine four-partite entanglement with two measurement settings only.