Density Matrix Calculator

Analyze quantum states using density matrix formalism

State Type:

Alpha (|0> coefficient):

Beta (|1> coefficient):

Density Matrix rho

[[1.0000, 0.0000]
[0.0000, 0.0000]]

Trace(rho)

1.0000

Purity Tr(rho^2)

1.0000

Pure State

Eigenvalues

lambda_1 = 1.0000, lambda_2 = 0.0000

Von Neumann Entropy S = -Tr(rho * log2(rho))

0.0000 bits

Bloch Vector (r_x, r_y, r_z)

(0.0000, 0.0000, 1.0000)

|r| = 1.0000 (1 = pure, 0 = maximally mixed)

rho = |psi> <psi| (pure state)

rho = sum_i p_i |psi_i> <psi_i| (mixed state)

Tr(rho) = 1, Tr(rho^2) <= 1

Pure state: Tr(rho^2) = 1, Mixed: Tr(rho^2) < 1