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A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference
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Real-space renormalization yields finite correlations.

Thomas Barthel1, Martin Kliesch, Jens Eisert

  • 1Institute for Physics and Astronomy, Potsdam University, 14476 Potsdam, Germany.

Physical Review Letters
|September 28, 2010
PubMed
Summary
This summary is machine-generated.

Multiscale entanglement renormalization Ansatz (MERA) states in quantum systems, except in 1D, are finite-correlation states. These efficiently contractible states obey the entanglement entropy area law.

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Area of Science:

  • Quantum Information Theory
  • Condensed Matter Physics
  • Computational Physics

Background:

  • Real-space renormalization methods are crucial for studying quantum lattice systems.
  • The multiscale entanglement renormalization Ansatz (MERA) is a hierarchical framework for these states.
  • Understanding the properties of MERA states, particularly their entanglement scaling, is key.

Purpose of the Study:

  • To classify MERA states within broader tensor network formalisms.
  • To determine if MERA states adhere to the entanglement entropy area law.
  • To explore the relationship between real-space renormalization and efficiently contractible tensor networks.

Main Methods:

  • Analysis of MERA states' correlation functions.
  • Comparison of MERA states with projected entangled pair states (PEPS).
  • Investigation of bond dimension scaling with system size.

Main Results:

  • MERA states, excluding 1D, are identified as PEPS with finite correlation length.
  • The bond dimension of these MERA-derived PEPS is independent of system size.
  • MERA states satisfy the area law for entanglement entropy.

Conclusions:

  • Real-space renormalization generates states with local effective degrees of freedom.
  • MERA represents an efficiently contractible class of PEPS obeying the area law.
  • Alternative efficiently contractible schemes that violate the area law also exist.