{
  "id": "2510.01156",
  "version": "v1",
  "published": "2025-10-01T17:44:49.000Z",
  "updated": "2025-10-01T17:44:49.000Z",
  "title": "Superpositions of Quantum Gaussian Processes",
  "authors": [
    "Lorenzo Braccini",
    "Sougato Bose",
    "Alessio Serafini"
  ],
  "comment": "27 pages, 4 figures; Any feedback is welcome",
  "categories": [
    "quant-ph"
  ],
  "abstract": "We generalise the Gaussian formalism of Continuous Variable (CV) systems to describe their interactions with qubits/qudits that result in quantum superpositions of Gaussian processes. To this end, we derive a new set of equations in closed form, which allows us to treat hybrid systems' unitary and open dynamics exactly (without truncation), as well as measurements (ideal and noisy). The $N$-qubits $n$-modes entangled states arising during such processes are named Gaussian-Branched Cat States (GCSs). They are fully characterised by their superposed phase-space quantities: sets of generalised complex first moments and covariance matrices, along with the qubit reduced density matrix (QRDM). We showcase our general formalism with two paradigmatic examples: i) measurement-based entanglement of two qubits via a squeezed, leaking, and measured resonator; ii) the generation of the Wigner negativity of a levitated nanoparticle undergoing Stern-Gerlach interferometry in a diffusive environment.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-10-01T17:44:49.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quantum gaussian processes",
      "superpositions",
      "levitated nanoparticle undergoing stern-gerlach interferometry",
      "treat hybrid systems",
      "qubit reduced density matrix"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}