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A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference
07:56

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference

Published on: September 5, 2019

Entanglement negativity in quantum field theory.

Pasquale Calabrese1, John Cardy, Erik Tonni

  • 1Dipartimento di Fisica dell'Università di Pisa and INFN, 56127 Pisa, Italy.

Physical Review Letters
|October 4, 2012
PubMed
Summary
This summary is machine-generated.

We developed a novel method to quantify negativity in quantum field theories. This approach, using path integrals and replica techniques, accurately measures entanglement in relativistic systems.

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A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference
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Area of Science:

  • Quantum Field Theory
  • Quantum Information
  • Condensed Matter Physics

Background:

  • Entanglement quantification is crucial for understanding quantum systems.
  • Relativistic quantum field theories present unique challenges for entanglement measures.
  • Previous methods for calculating negativity in extended systems were limited.

Purpose of the Study:

  • To develop a systematic method for extracting negativity in 1+1 dimensional relativistic quantum field theories.
  • To apply this method to conformal field theories and derive new analytical results.
  • To validate the theoretical findings against numerical simulations.

Main Methods:

  • Utilizing path integral formalism to construct the partial transpose of the reduced density matrix.
  • Employing a replica approach to calculate the trace norm, yielding logarithmic negativity.
  • Applying the derived formulas to systems with adjacent and disjoint intervals.

Main Results:

  • The method successfully reproduces standard results for pure states.
  • Derived an analytical expression for logarithmic negativity in conformal field theories for adjacent intervals: E~(c/4)ln[ℓ(1)ℓ(2)/(ℓ(1)+ℓ(2))].
  • Demonstrated that negativity for disjoint intervals is scale invariant, depending only on the harmonic ratio.

Conclusions:

  • The developed method provides a robust tool for quantifying entanglement negativity in relativistic quantum field theories.
  • The analytical results for conformal field theories offer new insights into entanglement structure.
  • The findings are consistent with numerical results, validating the theoretical framework.