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A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference
Published on: September 5, 2019
Universal geometric entanglement close to quantum phase transitions
1School of Physical Sciences, The University of Queensland, QLD 4072, Australia.
Physical Review Letters
|June 4, 2008
Summary
Replacing quantum states with product states during renormalization group transformations quantifies entanglement loss. This study proves global geometric entanglement diverges logarithmically near quantum critical points in 1D systems.
Area of Science:
- Quantum information theory
- Condensed matter physics
- Statistical mechanics
Background:
- Renormalization group (RG) transformations are crucial for understanding quantum systems, often leading to entanglement loss.
- The behavior of entanglement under RG flow, especially near quantum critical points, remains an active area of research.
Purpose of the Study:
- To quantitatively assess the impact of replacing quantum states with product states at each step of RG transformations.
- To provide analytical proofs for the behavior of global geometric entanglement in 1D translationally invariant quantum systems.
Main Methods:
- Application of successive renormalization group transformations to quantum states with finite correlation length.
- Analytical and general proofs for systems in one spatial dimension.
Main Results:
- Demonstrated that global geometric entanglement per region diverges logarithmically with correlation length (xi) near quantum critical points: (c/12)log(xi/epsilon).
- Derived an upper bound for critical global geometric entanglement in terms of a logarithmic function of region size (L).
Conclusions:
- Replacing quantum states with product states during RG transformations provides a quantifiable measure of entanglement loss.
- The study offers crucial insights into entanglement scaling near quantum criticality in 1D quantum systems.
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