During this semester, I have been attending an Information Theory Course at the Barcelona Graduate School of Mathematics, and the last part of the course has been devoted to Quantum Information Theory, at the hands of ICREA Professor Andreas Winter. The science of the very small, where interactions between matter and energy involves a discrete treatment of quantities, has fostered the development of a mathematical approach to the information that is held in the states of a quantum system. Due to the Heinsenberg uncertainty principle, it is impossible to measure the state of a quantum system, and hence express it in terms of classical information, i.e., bits.
One of the fundamental tools in quantum information theory is Verschränkung or entanglement, a phyisical phenomenon implying that the quantum state of a pair of entangled or correlated particles cannot be described separately. Entanglement was the topic of a paper by Albert Einstein in 1935, which came to be known as the EPR paradox: physical reality described by quantum mechanics is incomplete. An example is the following quantum system, in bra-ket notation:
The term entanglement was in fact coined by Erwin Schrödinger at the same year, when he thought of the problem of interpretation of quantum superposition applied to a cat’s life. The cat, viewed as a quantum system, can be simultaneously in two states: alive or dead. The experiment goes as follows: a cat, a flask of poison, and a radioactive source are placed in a sealed box. If an internal monitor detects radioactivity (i.e. a single atom decaying), the flask is shattered, releasing the poison that kills the cat. The Copenhagen interpretation of quantum mechanics implies that after a while, the cat is simultaneously alive and dead. Yet, when one looks in the box, one sees the cat either alive or dead, not both alive and dead. This poses the question of when exactly quantum superposition ends and reality collapses into one possibility or the other.