Question

I've read that if a state is a product state, the reduced density matrices are pure and if the state is entangled, the reduced density matrices are both mixed.

What would it mean if you had a system of two particles, and when you calculated the reduced density matrices, one was pure and one was mixed?

Answer 1

If the reduced density matrices of a system of two particles are one pure and one mixed, it means that the system is in an entangled state.

In entanglement, the particles become inseparably linked, and their properties become correlated.

Step-by-step explanation:

If the reduced density matrices of a system of two particles are one pure and one mixed, it means that the system is in an entangled state.

In entanglement, the particles become inseparably linked, and their properties become correlated.

The mixed reduced density matrix indicates that the information about one of the particles is uncertain, while the pure reduced density matrix indicates that the information about the other particle is known with certainty.

If the reduced density matrices of a system of two particles are one pure and one mixed, it means that the system is in an entangled state. In entanglement, the particles become inseparably linked, and their properties become correlated.