[SOLVED] QIC - Computational Quantum Physics - weak 6

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Exercise 1: Density Matrices

Consider a quantum system formed by N subsystems (spins, atoms, particles etc..) each described by its wave function ψ_i ∈ H^D where H^D is a D-dimensional Hilbert space.

• How do you write the total wave function of the system Ψ(ψ₁,…ψ_N)? Write a Fortran code to 1) describe such a system (N-body non interacting, separable pure state) and

2) a general N-body pure wave function Ψ ∈ H^DN. Comment on their efficiency.

• Given N=2, write the density matrix of a pure state Ψ, ρ = |ΨihΨ|.
• Given a generic density matrix in H^D2 compute the reduce density matrix of either the left or the right system, e.g. ρ₁ = Tr₂ ρ.
• Test the functions described before (and all others needed) on two-spin one-half (qubits) withdifferent states.

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