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This is a theoretical quantum many-body result. It proves that entanglement between distant regions of a gapped ground state vanishes beyond a finite length, and that in one dimension this property characterizes matrix product states. It is foundational rather than applied, but tensor-network methods built on MPS underpin many quantum simulation and classical-simulability tools, so the result bears on which states quantum hardware and classical algorithms can efficiently represent.
Entanglement Sudden Death in Gapped Ground States
arXiv:2610.17038v1 Announce Type: new Abstract: Spatial sudden death of entanglement refers to the disappearance of quantum correlations between subsystems after a certain distance called the entanglement length. Specifically, given a density matrix $\rho_{ABC}$ on a tripartite system $ABC$ with $B$ spatially separating $A$ and $C$, the entanglement length is the distance $\ell(A,C)$ after which the reduced density matrix $\rho_{AC}$, given by tracing out the $B$ subsystem, is separable. We show in the case of gapped ground states in any dimension that the entanglement length is finite on finite subsystems. Restricting to one-dimensional systems, we prove that normal matrix product states have a finite entanglement length independent of $A$ and $C$, and that a finite pure state with such uniform entanglement length has a matrix product state representation with bond dimension independent of $A$ and $C$. Consequently, in one dimension, entanglement length distinguishes matrix product states from all other pure states.
Abstract:Spatial sudden death of entanglement refers to the disappearance of quantum correlations between subsystems after a certain distance called the entanglement length. Specifically, given a density matrix $\rho_{ABC}$ on a tripartite system $ABC$ with $B$ spatially separating $A$ and $C$, the entanglement length is the distance $\ell(A,C)$ after which the reduced density matrix $\rho_{AC}$, given by tracing out the $B$ subsystem, is separable. We show in the case of gapped ground states in any dimension that the entanglement length is finite on finite subsystems. Restricting to one-dimensional systems, we prove that normal matrix product states have a finite entanglement length independent of $A$ and $C$, and that a finite pure state with such uniform entanglement length has a matrix product state representation with bond dimension independent of $A$ and $C$. Consequently, in one dimension, entanglement length distinguishes matrix product states from all other pure states.
Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech); Strongly Correlated Electrons (cond-mat.str-el); Mathematical Physics (math-ph)
arXiv:2610.17038 [quant-ph]
(or arXiv:2610.17038v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2610.17038 arXiv-issued DOI via DataCite (pending registration)
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