Tomography of a Macroscopic Quantum State influenced by Classical Self-Gravity

• URL: http://arxiv.org/abs/2607.06967v1
• Date: Wed, 08 Jul 2026 03:45:17 GMT
• Title: Tomography of a Macroscopic Quantum State influenced by Classical Self-Gravity
• Abstract summary: Macroscopic optomechanical systems offer a promising testbed for distinguishing whether gravity acts as a quantum interaction or as a classical field.<n>Based on SN theory, this work investigates how classical self-gravity affects continuous quantum state tomography.<n>We quantify the resulting QG-SN distinguishability via the Hellinger distance and analyse its dependence on measurement strength and temperature.
• Score: 9.475898235438367
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Macroscopic optomechanical systems offer a promising testbed for distinguishing whether gravity acts as a quantum interaction or as a classical field. Schrodinger-Newton (SN) theory is the nonrelativistic limit of semi-classical gravity where quantum matter couples to classical gravity. Based on SN theory, this work investigates how classical self-gravity affects continuous quantum state tomography of a macroscopic mechanical oscillator monitored by variable-angle homodyne detection. In the Schrodinger-Newton (SN) theory, the measurement record arises from a different conditional test mass dynamics from that in quantum-gravity (QG)/standard quantum mechanics, consequently, applying the QG-optimised reconstruction map introduces an additional state-dependent contribution. We show that this contribution makes the reconstructed covariance depend on the chosen set of tomography angles and can drive the SN covariance--after QG filtering--outside the standard Gaussian-covariance domain set by the Heisenberg uncertainty principle. We quantify the resulting QG-SN distinguishability via the Hellinger distance and analyse its dependence on measurement strength and temperature. We then formulate the same issue in the broader setting of nonlinear quantum mechanics: when the system's conditional dynamics during the readout process depends on the state being inferred, the tomographic map acquires nonlinear, model-dependent corrections to the usual Radon or Gaussian reconstruction map.

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