No Cloning Theorem in 5 mins

Further readings

The world of quantum mechanics has rules that we don’t normally see in the classical realm of our day-to-day life. In this video, Englert goes through a simple proof of one of these surprising rules, starting from the fundamental postulates of quantum mechanics. Discovered in 1982, the No-Cloning Theorem, which states that an unknown generic quantum state cannot be perfectly copied, underlies all quantum processes. It also resolved a much discussed problem at the time – whether it is possible to signal faster than light using quantum effects. The answer is no, thus, no violation of the principle of causality.

One direct consequence of the no-cloning theorem is how we deal with information in quantum computing. On our everyday computers, we can intermittently save progress of our work, or make copies of documents. But, because of the no-cloning rule, quantum computers don’t have that flexibility, requiring processes to be completed in a single run.

Another important issue lies in error correction in the presence of noise. Even in classical computers, checking and fixing errors is an entire industry in its own right, in case any information gets lost or corrupted. One of the common practices is to have secure backups of data regularly. However, because the no-cloning theorem disallows back-ups of our data, we have to be even more clever in how we perform the checks and balances needed for mitigating errors in quantum information. This is tackled by quantum error correction codes.

On the other hand, this inability to clone quantum states makes the construction of an universally secure communication channel possible, which forms the foundation of Quantum Cryptography. Consider a quantum state sent between two parties, with a spy trying to eavesdrop the communication. Because quantum states cannot be perfectly copied, it means that the spy cannot intercept the quantum state, measure it, and resend a copy of the quantum state perfectly.

The ubiquity of the no-cloning theorem finds relevance in all fields of quantum information, computing, and communication. By making use of these unusual properties of quantum states and processes, we can go beyond the limits of what’s possible with everyday classical devices, and this is part of why we are advancing quantum technologies as the next step in innovation.

Resolving faster-than-light communication: The no-cloning theorem was proven in response to a published proposal for using quantum entanglement to achieve faster-than-light communication. This idea violates the principles of causality. A simple formulation of the idea goes like this - imagine an entangled pair of particles, which are separated and carried away by two parties, Alice and Bob. Assuming that quantum cloning was permitted, Bob can make endless copies of his entangled particle, and continuously make measurements on each copy as soon as they are created.

Alice can then send information to Bob by simply measuring her particle. Before Alice makes her measurement, Bob will find that his sequence of measurements to be in a random distribution. However, as soon as Alice performs her measurement, Bob will now see that his measurements show only one possible outcome. In other words, Bob will immediately know when Alice performs her measurement, no matter how far separated they are!

Citations

Heshami, K., England, D. G., Humphreys, P. C., Bustard, P. J., Acosta, V. M., Nunn, J., & Sussman, B. J. (2016). Quantum Memories: Emerging Applications and recent advances. Journal of Modern Optics, 63(20), 2005–2028. https://doi.org/10.1080/09500340.2016.1148212

Roffe, J. (2019). Quantum Error Correction: An introductory guide. Contemporary Physics, 60(3), 226–245. https://doi.org/10.1080/00107514.2019.1667078

Wootters, W. K., & Zurek, W. H. (1982). A single quantum cannot be cloned. Nature, 299(5886), 802–803. https://doi.org/10.1038/299802a0

Nielsen, M. A., & Chuang, I. L. (2022). Quantum Computation and Quantum Information. Cambridge University Press.