How does the Planck scale affect qubits?

TL;DR

This paper investigates how quantum gravity effects at the Planck scale modify spin uncertainty relations, leading to new spin states and potential observable differences in qubits interacting with quantum background geometries.

Contribution

It introduces a novel model of nonlocal geometry that generalizes spin uncertainty relations and predicts new spin eigenstates influenced by quantum gravity effects.

Findings

New spin eigenstates with eigenvalues shifted by a small correction 2 to 3h.

Existence of entangled spin states linking particles and fluctuating spacetime.

Potential methods to empirically distinguish geometric qubits from canonical ones.

Abstract

Gedanken experiments in quantum gravity motivate generalised uncertainty relations (GURs) implying deviations from the standard quantum statistics close to the Planck scale. These deviations have been extensively investigated for the non-spin part of the wave function but existing models tacitly assume that spin states remain unaffected by the quantisation of the background in which the quantum matter propagates. Here, we explore a new model of nonlocal geometry in which the Planck-scale smearing of classical points generates GURs for angular momentum. These, in turn, imply an analogous generalisation of the spin uncertainty relations. The new relations correspond to a novel representation of {\rm SU(2)} that acts nontrivially on both subspaces of the composite state describing matter-geometry interactions. For single particles each spin matrix has four independent eigenvectors, corresponding to two $2$-fold degenerate eigenvalues $\pm (\hbar + \beta)/2$, where $\beta$ is a small correction to the effective Planck's constant. These represent the spin states of a quantum particle immersed in a quantum background geometry and the correction by $\beta$ emerges as a direct result of the interaction terms. In addition to the canonical qubits states, $\ket{0} = \ket{\uparrow}$ and $\ket{1} = \ket{\downarrow}$, there exist two new eigenstates in which the spin of the particle becomes entangled with the spin sector of the fluctuating spacetime. We explore ways to empirically distinguish the resulting `geometric' qubits, $\ket{0'}$ and $\ket{1'}$, from their canonical counterparts.