Nullifiers of non-Gaussian cluster states through homodyne measurement

• URL: http://arxiv.org/abs/2505.21066v2
• Date: Wed, 28 May 2025 08:19:04 GMT
• Title: Nullifiers of non-Gaussian cluster states through homodyne measurement
• Authors: Vojtěch Kala, Radim Filip, Petr Marek,
• Abstract summary: Non-Gaussian states must be embedded in a cluster state to reach universality and fault tolerance.<n>We propose a framework for the characterization of non-Gaussian cluster states.
• Score: 0.6554326244334868
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Multiplexing potential of large-scale optical Gaussian cluster states was already experimentally demonstrated. Non-Gaussian states must be embedded in a cluster state to reach universality and fault tolerance. Basic quantum operations with the potential to induce non-Gaussianity, such as photon subtraction, start to broaden the available experimental toolbox as well. The interplay of the two, non-Gaussian multimode cluster states, remains challenging both theoretically and experimentally. Here we propose a framework for the characterization of non-Gaussian cluster states. In analogy to the nowadays frequently used Gaussian nullifiers, we define non-Gaussian nullifiers of cluster states that enable certification of non-Gaussianity in the cluster state. We illustrate the concept with an example of a cluster state created from photon-subtracted squeezed states. The nullifier can be evaluated from a homodyne measurement, which is a natural detection for optical cluster states.

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