Quantum Spacetime: How Deformed Symmetries Create and Destroy Entanglement ✛
Context
Attempts to unify quantum mechanics and gravity lead to the idea that at the Planck scale, spacetime ceases to be smooth and acquires a quantum structure. One consequence is noncommutativity of coordinates, where the order of measuring position and time affects the outcome. In such models, symmetries, including Lorentz transformations, may be deformed, altering the conservation laws of energy and momentum for composite systems. Previous work showed that quantum spacetime causes fundamental decoherence of single particles, but effects on multiparticle systems remained unexplored. This paper fills that gap by considering two particles and analyzing the competition between the birth of correlations and their destruction.
Methods
The authors use the formalism of deformed symmetries within κ-Minkowski spacetime, where coordinates obey a noncommutative relation. They construct a model of two nonrelativistic particles, each described by two energy levels and in a superposition of momentum directions. From the deformed energy addition rule, they derive a Hamiltonian with an additional term proportional to the product of the particles' momenta. The evolution of the system is described by a Lindblad equation, where the dissipative term arises from the deformation of symmetries. To quantify correlations, they compute concurrence, l1-norm of coherence, quantum mutual information, and local quantum Fisher information.
Results
The model predicts that from an initially unentangled state (θ=0), two particles become entangled over time thanks to the deformed energy conservation law. The entanglement time is estimated as Tent = ℏ EQG / (2 m c² ε), where EQG is the Planck energy, m is the particle mass, and ε is the characteristic energy of the levels. For a pair of ions with mass on the order of 3.7×10¹⁰ eV and an energy scale of 1 eV, the entanglement time is about 214 seconds (approximately 3.6 minutes). However, decoherence caused by quantum spacetime eventually destroys entanglement: for all initial states except the maximally entangled one, concurrence goes to zero in finite time. At the same time, the l1-norm of coherence and quantum mutual information are asymptotically preserved for partially entangled initial states, indicating the survival of nonquantum and quantum correlations other than entanglement.
Implications
This work shows for the first time that deformed symmetries of quantum spacetime can not only destroy but also create quantum correlations in multiparticle systems. This distinguishes it from previous studies focused on single-particle decoherence. The mechanism of entanglement generation here is purely kinematic: it does not require physical interaction but arises from the modified energy addition rule. This opens a new channel for experimental searches for traces of quantum gravity, complementing known proposals for gravitationally induced entanglement.
Future development
A natural extension would be to generalize the model to N-particle systems, where the effects of deformed symmetries might be amplified or manifest differently. It is also important to investigate the influence of different κ-Poincaré bases and nonrelativistic limits on the dynamics of correlations. Experimental verification would require qubits with very long coherence times, such as trapped ions, where coherence times exceeding one hour have already been achieved.
Impact
The results may stimulate experiments in quantum optics and trapped-ion physics searching for deformations of conservation laws. They also affect the interpretation of quantum gravity as a source of fundamental decoherence, offering a more nuanced picture with competing effects.
Next steps
The next step will be to calculate correlations for systems of three or more particles, as well as to analyze sensitivity to the deformation parameter under realistic experimental conditions. It would also be useful to compare the model's predictions with other approaches to quantum spacetime, such as minimal-length models.
Key open problems
The paper is directly related to the problem of reconciling quantum mechanics and gravity, in particular the nature of spacetime at the Planck scale. It contributes to understanding how quantum correlations behave in the presence of fundamental decoherence, which is important for the interpretation of quantum theory. Furthermore, it touches on the long-standing problem of nonlocality in quantum gravity, showing that modified conservation laws can generate nonlocal effects observable as entanglement.
The knowledge machine's view
This section is addressed to the author of the paper and their colleagues. Neighbouring works were found by meaning-based search across our archive, not by word overlap. We do not review: we show the field around the work.
What the work does
The authors model two two-level particles in κ-Minkowski spacetime with deformed symmetries, derive a Hamiltonian with momentum-dependent interaction and a Lindblad equation to describe decoherence. They show that an initially unentangled state evolves into an entangled one in finite time, estimated at ~214 seconds for a pair of ions, but then decoherence destroys the entanglement while preserving other correlations, such as coherence and mutual information.
Where its strength is
This work is the first to demonstrate the competition between entanglement generation due to the deformed energy conservation law and its destruction due to decoherence in a many-particle system, opening a new avenue for laboratory tests of quantum gravity effects.
Where it could go next
- It might be interesting to compare the entanglement generation mechanism with a model where gravity induces entanglement with a delay, to clarify the role of noncommutativity and deformed symmetries.based on: Gravity Entangles Particles with a Delay arXiv:2606.12901
- Closely related is work on the influence of curved space on quantum correlations; one could consider how symmetry deformations in κ-Minkowski spacetime relate to background curvature effects in many-particle systems.based on: How Curved Space Changes the Rules of the Quantum Game arXiv:2607.05715
- One might explore connections with quantum causality models, where blurring of the causal structure affects the dynamics of correlations, to see how time noncommutativity could alter predictions for entanglement.based on: When a Quantum Particle Blurs Causality arXiv:2606.03671
Worth trying
- Test the predicted entanglement time on real trapped-ion systems, taking into account experimental constraints on decoherence.
- Check whether asymptotic coherence and mutual information persist for a broader class of initial states, including mixed states.
- Consider using quantum Fisher information as an observable to detect deformed symmetries in the laboratory.
Why this may matter
The proposed mechanism could serve as a basis for experimental tests of quantum gravity at scales accessible to modern quantum technologies, and also clarify the fundamental connection between spacetime symmetries and quantum correlations.
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The entanglement time for a pair of ions is estimated at just a few minutes, which is comparable to the preparation time of quantum states in modern laboratories. If the quantum-gravity scale grew with the number of particles, as suggested by the 'football' problem, the entanglement time would increase to hours, still within reach for long-lived qubits.
Key numbers
- entanglement time for a pair of ions: ≈ 214 s (3.6 min)
- ion mass in the estimate: 3.7×10¹⁰ eV
- characteristic energy of levels: 1 eV
- Planck energy: 1.2×10²⁸ eV
- deformation parameter in the model: ℓ = 1 (in units where m=1, ε=1)