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Updated: Sep 10, 2025
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A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference
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Optimal Bound on Long-Range Distillable Entanglement
Jonah Kudler-Flam1,2, Vladimir Narovlansky1, Nikita Sopenko1
1Institute for Advanced Study, School of Natural Sciences, Princeton, New Jersey 08540, USA.
Physical Review Letters
|August 27, 2025
Summary
We established an upper limit for distillable entanglement, showing it decays faster than 1/r with distance. This bound is strengthened to 1/r^D for rotationally invariant states in D dimensions.
Area of Science:
- Quantum Information Theory
- Condensed Matter Physics
Background:
- Entanglement is a key quantum resource.
- Understanding its long-range behavior is crucial for quantum technologies.
Purpose of the Study:
- To determine the fundamental limits on long-range distillable entanglement.
- To explore the spatial decay rates of entanglement in various quantum states.
Main Methods:
- Derivation of an upper bound for distillable entanglement in D spatial dimensions.
- Construction of explicit quantum states saturating this bound.
- Analysis of ground states of free fermion Hamiltonians.
Main Results:
- Distillable entanglement decays faster than 1/r with distance.
- For rotationally invariant states, decay is bounded by 1/r^D.
- Constructed states approach this bound, with 1D free fermion ground states achieving it.
- Conformal field theory states exhibit faster-than-polynomial decay.
Conclusions:
- Entanglement decay is fundamentally limited by spatial dimensions and symmetry.
- Explicit constructions demonstrate near-optimal long-range entanglement.
- Certain quantum states, like those in CFT, show significantly faster entanglement decay than predicted bounds.
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