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density-matrix [May 25, 2026 at 13:55] – external edit 127.0.0.1density-matrix [June 13, 2026 at 03:13] (current) – external edit 127.0.0.1
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 # Density matrix # Density matrix
-**Density matrix** (written as $\rho$) is a matrix representation of a quantum state that is strictly more general than the state vector $\lvert\psi\rangle$. While a state vector can only represent [[pure-state|pure states]], a density matrix can represent [[mixed-state|mixed states]] as well, making it the correct tool for open quantum systems, noisy circuits, and statistical ensembles of quantum states.+**Density matrix** (written as $\rho$) is a matrix representation of a quantum state
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 +It's a more general way to represent a quantum state compared to the [[state-vector|state vector]] $\lvert\psi\rangle$. While a state vector can only represent [[pure-state|pure states]], a density matrix can represent [[mixed-state|mixed states]] as well, making it the correct tool for open quantum systems, noisy circuits, and statistical ensembles of quantum states.
  
 Every pure state $\lvert\psi\rangle$ has a corresponding density matrix constructed by the outer product of the ket with its bra. Every pure state $\lvert\psi\rangle$ has a corresponding density matrix constructed by the outer product of the ket with its bra.
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 ## Time evolution ## Time evolution
-Under Hamiltonian evolution, the density matrix evolves according to the von Neumann equation $d\rho/dt = -i[H,\rho]/\hbar$. For open systems with environmental noise, this generalizes to the [[lindbald-equation|Lindblad master equation]], which adds dissipative terms describing decoherence and relaxation.+Under Hamiltonian evolution, the density matrix evolves according to the von Neumann equation $d\rho/dt = -i[H,\rho]/\hbar$. For open systems with environmental noise, this generalizes to the [[lindblad-equation|Lindblad master equation]], which adds dissipative terms describing decoherence and relaxation.
  
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