Quantum state transformation refers to the process by which a quantum system changes from one state to another. This transformation can occur through various mechanisms, such as measurement, interaction with other systems, or the application of quantum gates in quantum computing. The mathematical representation of these states is often done using vectors in a complex vector space, known as a Hilbert space. In quantum mechanics, these transformations are governed by unitary operators, which preserve the total probability of the system. When a quantum state is transformed, it can exhibit different properties, such as superposition and entanglement, which are fundamental to the behavior of quantum systems and technologies like quantum computing and quantum cryptography.