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Quantum 2.0 Conference and Exhibition

Experimental verification of Entanglement Witness of Dicke state on IBM QPU

Tomis Prajapati, Harsh Mehta, V. Narayanan

Published Jan 1, 2025• 0 citations
Publisher

Abstract

An entanglement witness is necessary to characterize genuine multipartite entan-gled states. We theoretically derive the entanglement witness for the four-qubit Dicke state. A negative expectation value confirms genuine multipartite entanglement. Our witness was experimentally verified on IBM QPU, with and without error mitigation techniques.

DOI
10.1364/quantum.2025.qtu3a.14

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An entanglement witness is necessary to characterize genuine multipartite entan-gled states. We theoretically derive the entanglement witness for the four-qubit Dicke state. A negative expectation value confirms genuine multipartite entanglement. Our witness was experimentally verified on IBM QPU, with and without error mitigation techniques.
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.
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.
We report on the experimental observation and characterization of a six-photon entangled Dicke state. We obtain a fidelity as high as 0.654+/-0.024 and prove genuine six-photon entanglement by, amongst others, a two-setting witness yielding -0.422+/-0.148. This state has remarkable properties; e.g., it allows obtaining inequivalent entangled states of a lower qubit number via projective measurements, and it possesses a high entanglement persistency against qubit loss. We characterize the properties of the six-photon Dicke state experimentally by detecting and analyzing the entanglement of a variety of multipartite entangled states.
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.
I present methods for detecting entanglement around symmetric Dicke states. In particular, I consider N-qubit symmetric Dicke states with N/2 excitations. I show that for large N these states have the smallest overlap possible with states without genuine multipartite entanglement. Thus these states are particularly well suited for the experimental examination of multipartite entanglement. I present fidelity-based entanglement witness operators for detecting multipartite entanglement around these states. I then consider entanglement criteria, somewhat similar to the spin squeezing criterion, based on the moments or variances of the collective spin operators. Surprisingly, these criteria are based on an upper bound for variances for separable states. I present criteria detecting entanglement in general and criteria detecting only genuine multipartite entanglement. The collective operator measured for this criteria is an important physical quantity: Its expectation value essentially gives the intensity of the radiation when a coherent atomic cloud emits light.