Consider two quantum states states described via the density operators and . Then the composite state describing the total system is described via the tensor product

This operation between finite and discrete matrices is also called the Kronecker product.

Let us build a separable composite density matrix "by hand." Using np.kron or otherwise, complete the function below that returns the density matrix describing a composite system, given the density matrices rho and sigma that describe the individual systems.

def composite_density_matrix(rho, sigma):
"""Build composite density matrix from two states.
Args:
rho: (np.array(array[complex]): The density matrix of the first input state
sigma: (np.array(array[complex]): The density matrix of the second input state
Returns:
(np.array([array[complex]])): The density matrix for the composite system.
"""

################
#YOUR CODE HERE#
################

# Build the density matrix and return it
return


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Learning Objectives:

  • Understand and predict the behavior of a subsystem in a composite quantum system.
  • Compute the reduced state via the partial trace operation.
  • Use the purification theorem to map a mixed state into a pure state.