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arXiv:2604.27170

Light-Cone Structure of Propagation of Entanglement

Israel Michael Sigal

quant-phmath-phmath.FASubmitted Apr 29, 2026• Announced May 1, 2026• 0 citations
v1 · Apr 29, 2026v2 · Jun 9, 2026
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Abstract

For a wide class of bipartite systems with localized couplings, we establish existence of an effective light-cone for propagation of entanglement. This result yields a hard lower bound on the time it takes, under ideal conditions (no loss, no decoherence), to transport entanglement to a distant location (say, a node of a graph-structured quantum network), or to maintain it there.

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For a wide class of bipartite systems with localized couplings, we establish existence of an effective light-cone for propagation of entanglement. This result yields a hard lower bound on the time it takes, under ideal conditions (no loss, no decoherence), to transport entanglement to a distant location (say, a node of a graph-structured quantum network), or to maintain it there.
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In a bipartite system subject to decoherence from two separate reservoirs, entanglement is typically destroyed faster than where there is a single reservoir. Surprisingly, however, the existence of separate reservoirs can also have a beneficial entangling effect: if the qubits are coupled and driven externally by a classical field, the system ends in a stationary state characterized by a finite degree of entanglement. This phenomenon occurs only in a certain region of the parameter space and the structure of the stationary state has a universal form which does not depend on the initial state or on the specific physical realization of the qubits. We show that the entanglement thus generated can be propagated within a quantum network using simple local unitary operations. We suggest the use of such systems as 'batteries of entanglement' in quantum circuits.
In a bipartite system subject to decoherence from two separate reservoirs, entanglement is typically destroyed faster than where there is a single reservoir. Surprisingly, however, the existence of separate reservoirs can also have a beneficial entangling effect: if the qubits are coupled and driven externally by a classical field, the system ends in a stationary state characterized by a finite degree of entanglement. This phenomenon occurs only in a certain region of the parameter space and the structure of the stationary state has a universal form which does not depend on the initial state or on the specific physical realization of the qubits. We show that the entanglement thus generated can be propagated within a quantum network using simple local unitary operations. We suggest the use of such systems as 'batteries of entanglement' in quantum circuits.
The speed limit of information propagation is one of the most fundamental features in non-equilibrium physics. The region of information propagation by finite-time dynamics is approximately restricted inside the effective light cone that is formulated by the Lieb-Robinson bound. To date, extensive studies have been conducted to identify the shape of effective light cones in most experimentally relevant many-body systems. However, the Lieb-Robinson bound in the interacting boson systems, one of the most ubiquitous quantum systems in nature, has remained a critical open problem for a long time. This study reveals a tight effective light cone to limit the information propagation in interacting bosons, where the shape of the effective light cone depends on the spatial dimension. To achieve it, we prove that the speed for bosons to clump together is finite, which in turn leads to the error guarantee of the boson number truncation at each site. Furthermore, we applied the method to provide a provably efficient algorithm for simulating the interacting boson systems. The results of this study settle the notoriously challenging problem and provide the foundation for elucidating the complexity of many-body boson systems.
Abstract In this paper, we revisit a “relatively local” model proposed in [1], where locality and dimensionality of space only emerges from the entanglement structure of the state the system is in. Various quantities such as butterfly velocity/entanglement speed can be defined similarly, at least in the regime where locality is well defined and a light cone structure emerges in the correlation between sites. We find that the relations observed between them in local models [2] are not respected. In particular, we conjecture that the hierarchy of the interaction over different distances provides different “layers” of light cones. When long range interactions are sufficiently suppressed, the effective light cones are dominated by linear behaviour with little remnant of non-locality. This could potentially be used as a physical smoking gun for emergent locality in non-local models.