Class DensityMatrix

java.lang.Object
org.episteme.natural.physics.quantum.DensityMatrix
public class DensityMatrix extends Object
Represents a density matrix $\rho$ for mixed quantum states.

$\rho = \sum_i p_i |\psi_i\rangle\langle\psi_i|$ where $p_i$ is probability, and $\sum p_i = 1$.

Since:
1.0
Author:
Silvere Martin-Michiellot, Gemini AI (Google DeepMind)

  • Constructor Details

  • Method Details

    • fromPureState

      public static DensityMatrix fromPureState(BraKet psi)
      Creates a pure state density matrix $|\psi\rangle\langle\psi|$.

    • purity

      public Real purity()
      Calculates the Purity $\gamma = Tr(\rho^2)$. For pure states, Purity = 1. For mixed states, invalid input: '<' 1.

    • amplitudeDamping

      public DensityMatrix amplitudeDamping(Real gamma)
      Applies amplitude damping (T1 decay) channel. Models energy dissipation to environment.
      Parameters:
      gamma - Decay probability (0 to 1)
      Returns:
      New density matrix after damping

    • phaseDamping

      public DensityMatrix phaseDamping(Real gamma)
      Applies phase damping (T2 dephasing) channel. Models loss of phase coherence without energy loss.
      Parameters:
      gamma - Dephasing probability (0 to 1)
      Returns:
      New density matrix after dephasing

    • depolarize

      public DensityMatrix depolarize(Real p)
      Depolarizing channel. ρ → (1-p)ρ + (p/3)(XρX + YρY + ZρZ)
      Parameters:
      p - Error probability
      Returns:
      Depolarized density matrix

    • vonNeumannEntropy

      public Real vonNeumannEntropy()
      Von Neumann entropy: S(ρ) = -Tr(ρ log ρ) For pure states S = 0, for maximally mixed S = log(d)
      Returns:
      Entropy in nats (use log base e)

    • getMatrix

      public DenseMatrix<Complex> getMatrix()