Coherence and Entanglement in a Non-commutative Spacetime

TL;DR

The paper analyzes a two-particle system in a non-commutative spacetime with deformed energy-momentum composition, showing that a momentum-dependent Hamiltonian term can generate entanglement even as Lindblad-type decoherence tends to destroy it. By decomposing the dynamics into Hamiltonian and dissipative parts and introducing two deformation scales, $\\ell_H$ and $\\ell_L$, the work reveals regimes where entanglement can intermittently arise and persist, while coherence, mutual information, and Local Quantum Fisher Information exhibit complementary, longer-lived correlations. The results highlight a subtle interplay between open-system decoherence and nonlocal energy conservation, suggesting that quantum gravity effects could be probed through coherence and correlation dynamics in engineered two-qubit systems. The findings have implications for testing Planck-scale physics and motivate extensions to multi-partite scenarios and experimental platforms with long coherence times.

Abstract

We investigate the emergence of quantum coherence and quantum correlations in a two-particle system with deformed symmetries arising from the quantum nature of spacetime. We demonstrate that the deformation of energy-momentum composition induces a momentum-dependent interaction that counteracts the decoherence effects described by the Lindblad equation in quantum spacetime. This interplay leads to the formation of coherence, entanglement and other correlations, which we quantify using concurrence, the $l_1$-norm of coherence, quantum mutual information and Local Quantum Fisher Information. Our analysis reveals that while the openness of quantum spacetime ultimately degrades entanglement, it also facilitates the creation and preservation of both classical and quantum correlations.

Figures (9)

• Figure 1: Concurrence for different initial conditions determined by $\theta$. The parameters used are $\ell = 1$, $m = 1$, $\epsilon = 1$, and $\omega = 0.5$.
• Figure 2: The $l_1$-norm of coherence for different initial conditions determined by $\theta$. The parameters used are $\ell = 1$, $m = 1$, $\epsilon = 1$, and $\omega = 0.5$.
• Figure 3: Behavior of the average density matrix elements $\bar{\rho}_{ij}$ for the initial condition $\theta=0$ and $\theta=\pi/12$. We assume parameters $\ell=1$, $m=1$, $\epsilon=1$, $\omega=0.5$.
• Figure 4: Quantum Mutual Information for different initial conditions determined by $\theta$. We assume parameters $\ell=1$, $m=1$, $\epsilon=1$, $\omega=0.5$.
• Figure 5: Comparison of the different quantifiers for coherence, quantum mutual information and entanglement studied in the paper for $\theta = 0$. The red/dotted curve represents the $l_1$-norm of coherence. The blue/dash-dotted curve represents quantum mutual information. The black/solid curve represents concurrence.