Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2602.20694 · Letters in Mathematical Physics

Spatial Entanglement Sudden Death in Spin Chains at All Temperatures

Samuel O. Scalet

quant-phcond-mat.stat-mechmath-phSubmitted Feb 24, 2026• Announced Feb 25, 2026• 0 citations
arXivHTMLPDF

Abstract

We prove a finite entanglement length for the Gibbs state of any local Hamiltonian on a spin chain at any finite temperature: After removing an interval of size at least equal to the entanglement length, the remaining left and right half-chains are in a separable state.
Comments
19 pages, 2 figures

Related papers

Entanglement Sudden Death in Gapped Ground States

Robert Ferydouni, Thomas Jackson, Samuel O. Scalet

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 $ρ_{ABC}$ 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 $ρ_{AC}$, 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.

quant-pharXiv:2610.17038•Oct 13, 2026•0 citations

Entanglement in quantum spin chains is strictly finite at any temperature

Ainesh Bakshi, Soonwon Choi, Saúl Pilatowsky-Cameo

Entanglement is the hallmark of quantum physics, yet its characterization in interacting many-body systems at thermal equilibrium remains one of the most important challenges in quantum statistical physics. We prove that the Gibbs state of any quantum spin chain can be exactly decomposed into a mixture of matrix product states with a bond dimension that is independent of the system size, at any finite temperature. As a consequence, the Schmidt number, arguably the most stringent measure of bipartite entanglement, is strictly finite for thermal states, even in the thermodynamic limit. Our decomposition is explicit and is accompanied by an efficient classical algorithm to sample the resulting matrix product states.

quant-pharXiv:2602.13386•Feb 17, 2026•0 citations

Localizable entanglement

M. Popp, Frank Verstraete, Miguel Angel Martin-Delgado +1 more

We consider systems of interacting spins and study the entanglement that can be localized, on average, between two separated spins by performing local measurements on the remaining spins. This concept of localizable entanglement (LE) leads naturally to notions like entanglement length and entanglement fluctuations. For both spin-$1∕2$ and spin-1 systems, we prove that the LE of a pure quantum state can be lower bounded by connected correlation functions. We further propose a scheme, based on matrix-product states and the Monte Carlo method, to efficiently calculate the LE for quantum states of a large number of spins. The virtues of LE are illustrated for various spin models. In particular, characteristic features of a quantum phase transition such as a diverging entanglement length can be observed. We also give examples for pure quantum states exhibiting a diverging entanglement length but finite correlation length. We have numerical evidence that the ground state of the antiferromagnetic spin-1 Heisenberg chain can serve as a perfect quantum channel. Furthermore, we apply the numerical method to mixed states and study the entanglement as a function of temperature.

arXiv:quant-ph/0411123•Physical Review A•Apr 4, 2005•244 citations

One-dimensional quantum Gibbs states in constant circuit depth

Saúl Pilatowsky-Cameo, Georgios Styliaris, Ainesh Bakshi +1 more

We prove that the Gibbs state of any spin chain can be exactly decomposed into a mixture of product states over contiguous blocks of qubits with bounded length, at any constant temperature. As a consequence, any such Gibbs state can be prepared by local unitary circuits of constant depth, with efficient classical preprocessing. We place strong limits on the spatial structure of thermal entanglement: both the entanglement depth and entanglement width (measures of multiparticle entanglement) are bounded by constants, while the localizable entanglement (the bipartite entanglement that can be generated with the aid of local measurements and classical communication) vanishes exactly beyond a constant threshold distance. Our result also has implications for quantum thermalization: for any translation-invariant spin-chain Hamiltonian with nondegenerate spectral gaps, typical low-complexity pure states drawn from a maximally entropic ensemble at any constant effective temperature become locally indistinguishable from the Gibbs state upon unitary evolution. Additionally, we obtain an analogous decomposition for fermionic systems: the Gibbs state of any 1D local fermionic Hamiltonian is exactly a mixture of constant-depth local fermionic circuits acting on Gaussian states.

quant-pharXiv:2609.35973•Sep 30, 2026•0 citations

Any Quantum Many-Body State under Local Dissipation will be Disentangled in Finite Time

Zongping Gong, Yuto Ashida

We prove that any quantum many-spin state under genetic local dissipation will be fully separable after a finite time independent of the system size. Such a sudden death of many-body entanglement occurs universally provided that there is a finite damping gap and the unique steady-state density matrix is of full rank. This result is rigorously derived by combining a state-reconstruction identity based on random measurements and the convergence bound for quantum channels. Related works and possible generalizations are also discussed.

arXiv:2409.12639•Sep 19, 2024•0 citations

Sharp universal death of entanglement threshold for Pauli Hamiltonians

Bobak T. Kiani

We determine the exact universal high-temperature separability threshold for Pauli Hamiltonians of bounded degree $Δ\ge2$. If every coefficient in the Hamiltonian has magnitude at most one and each term has overlapping support with at most $Δ$ other terms, the Gibbs state is a mixture of product Pauli eigenstates whenever \[ β\le z_Δ:= \operatorname{arctanh}\left[\max_{0\le x \le 1}x\left(\frac{1-x}{1+x}\right)^{Δ-1} \right]. \] For every $β>z_Δ$, a finite commuting Hamiltonian with maximum overlap degree at most $Δ$ has an entangled Gibbs state. At any fixed $β<z_Δ$ strictly below the threshold, a classical polynomial-time algorithm produces samples from a distribution over product Pauli eigenstates approximating the Gibbs state in trace distance.

quant-pharXiv:2609.30149•Sep 25, 2026•0 citations
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 ρABCρ_{ABC}ρABC​ on a tripartite system ABCABCABC with BBB spatially separating AAA and CCC, the entanglement length is the distance ℓ(A,C)\ell(A,C)ℓ(A,C) after which the reduced density matrix ρACρ_{AC}ρAC​, given by tracing out the BBB 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 AAA and CCC, and that a finite pure state with such uniform entanglement length has a matrix product state representation with bond dimension independent of AAA and CCC. Consequently, in one dimension, entanglement length distinguishes matrix product states from all other pure states.
Entanglement is the hallmark of quantum physics, yet its characterization in interacting many-body systems at thermal equilibrium remains one of the most important challenges in quantum statistical physics. We prove that the Gibbs state of any quantum spin chain can be exactly decomposed into a mixture of matrix product states with a bond dimension that is independent of the system size, at any finite temperature. As a consequence, the Schmidt number, arguably the most stringent measure of bipartite entanglement, is strictly finite for thermal states, even in the thermodynamic limit. Our decomposition is explicit and is accompanied by an efficient classical algorithm to sample the resulting matrix product states.
We consider systems of interacting spins and study the entanglement that can be localized, on average, between two separated spins by performing local measurements on the remaining spins. This concept of localizable entanglement (LE) leads naturally to notions like entanglement length and entanglement fluctuations. For both spin-1∕21∕21∕2 and spin-1 systems, we prove that the LE of a pure quantum state can be lower bounded by connected correlation functions. We further propose a scheme, based on matrix-product states and the Monte Carlo method, to efficiently calculate the LE for quantum states of a large number of spins. The virtues of LE are illustrated for various spin models. In particular, characteristic features of a quantum phase transition such as a diverging entanglement length can be observed. We also give examples for pure quantum states exhibiting a diverging entanglement length but finite correlation length. We have numerical evidence that the ground state of the antiferromagnetic spin-1 Heisenberg chain can serve as a perfect quantum channel. Furthermore, we apply the numerical method to mixed states and study the entanglement as a function of temperature.
We prove that the Gibbs state of any spin chain can be exactly decomposed into a mixture of product states over contiguous blocks of qubits with bounded length, at any constant temperature. As a consequence, any such Gibbs state can be prepared by local unitary circuits of constant depth, with efficient classical preprocessing. We place strong limits on the spatial structure of thermal entanglement: both the entanglement depth and entanglement width (measures of multiparticle entanglement) are bounded by constants, while the localizable entanglement (the bipartite entanglement that can be generated with the aid of local measurements and classical communication) vanishes exactly beyond a constant threshold distance. Our result also has implications for quantum thermalization: for any translation-invariant spin-chain Hamiltonian with nondegenerate spectral gaps, typical low-complexity pure states drawn from a maximally entropic ensemble at any constant effective temperature become locally indistinguishable from the Gibbs state upon unitary evolution. Additionally, we obtain an analogous decomposition for fermionic systems: the Gibbs state of any 1D local fermionic Hamiltonian is exactly a mixture of constant-depth local fermionic circuits acting on Gaussian states.
We prove that any quantum many-spin state under genetic local dissipation will be fully separable after a finite time independent of the system size. Such a sudden death of many-body entanglement occurs universally provided that there is a finite damping gap and the unique steady-state density matrix is of full rank. This result is rigorously derived by combining a state-reconstruction identity based on random measurements and the convergence bound for quantum channels. Related works and possible generalizations are also discussed.
We determine the exact universal high-temperature separability threshold for Pauli Hamiltonians of bounded degree Δ≥2Δ\ge2Δ≥2. If every coefficient in the Hamiltonian has magnitude at most one and each term has overlapping support with at most ΔΔΔ other terms, the Gibbs state is a mixture of product Pauli eigenstates whenever β≤zΔ:=arctanh⁡[max⁡0≤x≤1x(1−x1+x)Δ−1]. β\le z_Δ:= \operatorname{arctanh}\left[\max_{0\le x \le 1}x\left(\frac{1-x}{1+x}\right)^{Δ-1} \right]. β≤zΔ​:=arctanh[max0≤x≤1​x(1+x1−x​)Δ−1]. For every β>zΔβ>z_Δβ>zΔ​, a finite commuting Hamiltonian with maximum overlap degree at most ΔΔΔ has an entangled Gibbs state. At any fixed β<zΔβ<z_Δβ<zΔ​ strictly below the threshold, a classical polynomial-time algorithm produces samples from a distribution over product Pauli eigenstates approximating the Gibbs state in trace distance.