An optimal bound on long-range distillable entanglement

• URL: http://arxiv.org/abs/2504.02926v1
• Date: Thu, 03 Apr 2025 18:00:00 GMT
• Title: An optimal bound on long-range distillable entanglement
• Authors: Jonah Kudler-Flam, Vladimir Narovlansky, Nikita Sopenko,
• Abstract summary: We prove an upper bound on distillable entanglement in $D$ dimensions.<n>For states that are rotationally invariant, the bound is strengthened to $1/rD$.<n>Curiously, spatial states in conformal field theory are far from saturation, with distillable entanglement decaying faster than any.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We prove an upper bound on long-range distillable entanglement in $D$ spatial dimensions. Namely, it must decay faster than $1/r$, where $r$ is the distance between entangled regions. For states that are asymptotically rotationally invariant, the bound is strengthened to $1/r^D$. We then find explicit examples of quantum states with decay arbitrarily close to the bound. In one dimension, we construct free fermion Hamiltonians with nearest neighbor couplings that have these states as ground states. Curiously, states in conformal field theory are far from saturation, with distillable entanglement decaying faster than any polynomial.

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