Abstract
We show that an interaction between a harmonic oscillator and a two-level test mass (TLTM) mediated by a local operations and classical communication (LOCC) channel produces a signature that in (D. Carney et al., PRX Quantum 2, 030330 (2021)) is claimed to be exclusively reserved for channels that can transmit quantum information. We provide an explicit example based on a measurement-and-feedback channel, explain where the proof of Carney et al. fails, discuss to what degree setups of this type can test the nature of the gravitational interaction and remark on some fundamental implications that an LOCC model of gravity may have in black hole physics.
Highlights
The reconciliation of quantum mechanics and gravity is a long-standing open problem in physics, but progress towards a satisfying solution has long been hindered by the inaccessibility of the necessary experimental conditions
We explicitly construct a local operations and classical communications (LOCC) channel between a harmonic oscillator and a particle in a double-well potential, that is fully compatible with the conditions of the proof in [27] and reproduces the collapseand-revival dynamics in the interferometric signal
To find a separable Kraus representation for the LOCC model presented in the previous section we start with Equation (19)
Summary
The reconciliation of quantum mechanics and gravity is a long-standing open problem in physics, but progress towards a satisfying solution has long been hindered by the inaccessibility of the necessary experimental conditions. We explicitly construct a local operations and classical communications (LOCC) channel between a harmonic oscillator and a particle in a double-well potential, that is fully compatible with the conditions of the proof in [27] and reproduces the collapseand-revival dynamics in the interferometric signal. This allows us to identify the error in the proof and leads us to the conclusion that the protocol presented in [27] does not constitute a sufficient test to determine the nature of the gravitational interaction.
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