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Glossary

Quantum glossary

Density matrix

Also: density operator, ρ

A matrix description of a quantum state that can also represent uncertainty about which state you have.

Pure states give ρ = |ψ⟩⟨ψ|; mixtures give a weighted sum. The off-diagonal entries (“coherences”) are what decoherence destroys. It is the natural language for noise, and for one part of an entangled system.

ρ = Σᵢ pᵢ |ψᵢ⟩⟨ψᵢ|, Tr ρ = 1

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Related terms

  • Mixed state — A state that is a statistical mixture of pure states, describing classical uncertainty on top of quantum uncertainty.
  • Decoherence — The loss of quantum behaviour as a system becomes entangled with its uncontrolled environment.