nLab quantum systems -- contents

quantum logic

• linear logic, dependent linear type theory

  string diagrams in †-compact categories

  tensor networks

• Bohr topos

  order-theoretic structure

• quantum probability

quantum physics

• quantum systems

  (parameterized, open)

  quantum measurement

  quantum state collapse

  quantum decoherence

  quantum adiabatic theorem

  Berry phases

  Dyson formula

• quantum many-body physics

• quantum field theory

  functorial quantum field theory

  algebraic quantum field theory

  (non-)perturbative quantum field theory

• solid state physics

  quantum material

  (topological) phases of matter

quantum probability theory – observables and states

• states

  • classical state

  • quantum state

    • space of states (in geometric quantization)

    • state on a star-algebra, quasi-state

    • qbit, Bell state

      dimer, tensor network state

    • quantum state preparation

    • probability amplitude, quantum fluctuation

    • pure state

      • wave function

      • bra-ket

      • Bell state

    • quantum superposition, quantum interference

    • quantum entanglement

    • quantum measurement

      wave function collapse

      Born rule

      deferred measurement principle

      quantum reader monad

      measurement problem

    • superselection sector

    • mixed state, density matrix

      entanglement entropy

      holographic 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

  • Wigner's theorem

  • no-cloning theorem

  • Bell's theorem

quantum information

• quantum information via dagger-compact categories

• quantum operation, quantum channel

• quantum teleportation

• quantum entanglement

• entanglement entropy

  holographic entanglement entropy

  topological entanglement entropy

quantum technology

• quantum sensing

• quantum communication

• quantum cryptography

• quantum machine learning

quantum computing

• qbit, qdit

• quantum gate, quantum circuit

• adiabatic quantum computation

• measurement-based quantum computation

• topological quantum computation

• quantum programming language

• quantum error correction

  • HaPPY code

  • Majorana dimer code

• spin resonance qbit

• quantum algorithms:

  • Grover's algorithm

  • Shor's algorithm