nLab
entanglement entropy

Idea

entropy induced by entanglement in quantum physics, really a synonym for subsystem entropy

Related concepts

• tensor network

• holographic entanglement entropy

• black hole entropy via AdS-CFT duality

quantum probability theory – observables and states

• states

  • classical state

  • quantum state

    • space of states (in geometric quantization)

    • state on a star-algebra, quasi-state

    • probability amplitude, quantum fluctuation

    • pure state

      • wave function

        • bra-ket

        • wave function collapse

    • superposition, quantum interference

    • superselection sector

    • mixed state, density matrix

      entanglement entropy

    • coherent quantum state

  • ground state, excited state

  • quasi-free state

  • Fock space, second quantization

  • vacuum, vacuum state

    • Hadamard state

    • vacuum diagram

    • vacuum expectation value, vacuum amplitude, vacuum fluctuation

    • vacuum energy

    • vacuum polarization

    • interacting vacuum

    • thermal vacuum, KMS state

    • vacuum stability

      • false vacuum, tachyon, Coleman-De Luccia instanton

    • theta vacuum

    • perturbative string theory vacuum

      • non-geometric string theory vacuum

      • landscape of string theory vacua

  • entangled state

  • tensor network state

    • matrix product state

    • tree tensor network state

• observables

  • quantum observable, beable

  • algebra of observables, star-algebra

  • Bohr topos

  • quantum operator (in geometric quantization)

  • quantum operation, quantum effect, effect algebra

  • in quantum field theory

    • local observable

    • polynomial observable

      • linear observable

        • field observable

    • regular observable

    • microcausal observable

    • normal-ordered product, time-ordered products, retarded product

    • Wick algebra

    • scattering amplitude

    • interacting field algebra of observables, Bogoliubov's formula

• GNS construction

• theorems

  • order-theoretic structure in quantum mechanics

    • Gleason's theorem

    • Alfsen-Shultz theorem

    • Harding-Döring-Hamhalter theorem

    • Kochen-Specker theorem

    • Nuiten's lemma

  • no-cloning theorem

  • Bell's theorem

References

• Matthew Headrick, Lectures on entanglement entropy in field theory and holography (arXiv:1907.08126)

In AQFT:

• Roberto Longo, Feng Xu, Von Neumann Entropy in QFT (arxiv:1911.09390)

See also

• Wikipedia, Entropy of entanglement