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Glossary

Quantum glossary

Entanglement entropy

Also: von Neumann entropy, area law, volume law

A number, in bits, for how entangled one part of a pure quantum state is with the rest.

It is the entropy of the part on its own: zero when the two parts are unentangled, and at most the size of the smaller part. When it grows with the size of the region the state follows a volume law; when it grows only with the boundary, an area law. It measures entanglement only for pure states — for a mixed state it also counts ordinary classical uncertainty.

S(A) = −Tr(ρ_A log₂ ρ_A)

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Related terms

  • Entanglement — A correlation between quantum systems so strong that the whole has a definite state while the parts do not.
  • Density matrix — A matrix description of a quantum state that can also represent uncertainty about which state you have.
  • Mixed state — A state that is a statistical mixture of pure states, describing classical uncertainty on top of quantum uncertainty.
  • Measurement-induced phase transition — A sharp change in how entangled a quantum circuit’s state is, as the rate of mid-circuit measurements crosses a critical value.