Quantum nature of black hole and the superposition of fermionic field

The operational framework for the superposition of spacetime is fundamentally important in developing a comprehensive description of quantum gravity (Foo et al. in Phys Rev Lett 129:181301, 2022). As a “bottom-up” unifying theory of quantum gravity, it allows us to investigate how mass superposition of spacetime influences the performance of quantum information processing. In this paper, we study how the quantum-gravitational effects produced by the mass superposition of a black hole influence the quantum coherence of fermionic fields. It is shown that the spacetime effects associated with a classical black hole lead to inevitable decoherence. Notably, compared to classical black hole spacetime scenarios, fermionic fields near a black hole with superposed masses can retain more quantum coherence. This suggests that the quantum properties of spacetime may serve as resources to mitigate coherent degradation caused by gravitational effects. The bottom-up perspective on spacetime superposition proposed in this work serves as an indication of quantum-gravitational effects and holds significant theoretical implications.