Superpositions of Quantum Gaussian Processes

• URL: http://arxiv.org/abs/2510.01156v1
• Date: Wed, 01 Oct 2025 17:44:49 GMT
• Title: Superpositions of Quantum Gaussian Processes
• Authors: Lorenzo Braccini, Sougato Bose, Alessio Serafini,
• Abstract summary: 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.<n>We derive a new set of equations in closed form, which allows us to treat hybrid systems' unitary and open dynamics exactly.<n>We showcase our general formalism with two paradigmatic examples.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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