The Postulates of Quantum Mechanics

"Elements," the great compilation produced by Euclid of Alexandria in Ptolemaic Egypt circa 300 BC, established a unique logical structure for mathematics whereby every mathematical theory is built upon elementary axioms and definitions for which propositions and proofs follow. Theories in physics also take a similar structure. For example, classical mechanics is based on Sir Isaac Newton’s three laws of motion. Called “laws”, they are in fact elementary hypotheses—that is, axioms. While this may seem a remarkably different custom in physics compared to its mathematical counterpart, it should not be surprising to refer to assumptions as laws or principles because they provide physical theories with logical foundation and are functional to determine whether Nature has been described properly or they have a mere existence as an intellectual framework. After all, the true value of a physical science is to understand Nature.

Embracing the wave-particle duality and the complementarity principle, quantum mechanics has been founded on the three fundamental postulates. The founders of quantum mechanics could have been more ambitious to call these laws instead of plain postulates, but each of these three defies our intuition to such an extent that “postulates” sounds more natural.

In this collection of tutorial documents, detailed are the physical aspects of each postulate and their relevance to quantum computation and quantum information.

See also Chapter 1 of the