The statement "quantum information cannot be destroyed" refers to a principle in quantum mechanics known as the no-cloning theorem and the conservation of quantum information.
In classical computing, it is possible to make copies of information. For example, if you have a digital file, you can easily create multiple copies of that file. However, in the quantum realm, things work differently due to the fundamental principles of quantum mechanics.
The no-cloning theorem states that it is impossible to create an identical copy of an arbitrary unknown quantum state. In other words, you cannot take an arbitrary quantum state and produce an exact replica of it. This theorem is a consequence of the linearity and unitarity of quantum mechanics.
This principle implies that when you perform a measurement on a quantum system, extracting information from it, the original quantum state is fundamentally altered or disturbed. The act of measurement collapses the quantum state into a particular outcome, and the information about the other possible outcomes is lost.
While the specific outcome of a measurement may be random, the conservation of quantum information ensures that the total amount of information remains intact. The information is transformed or redistributed in a different form rather than being destroyed. This conservation of quantum information is a fundamental principle in quantum mechanics.
In practical terms, this principle has important implications for quantum information processing, such as quantum cryptography and quantum computing. It ensures the security of quantum communication protocols, where eavesdropping attempts would be detected due to the disturbance caused by measurement. Additionally, it underlies the reversibility and coherence preservation required for quantum computation.