Evolving into 1⁄2 x2 + 1⁄2 x3 is not a quantum operation that can occur in a closed system (it requires at the very least tracing over an auxiliary qubit).
Evolving into 1⁄2 x2 + 1⁄2 x3 is not a quantum operation that can occur in a closed system (it requires at the very least tracing over an auxiliary qubit).