A Very Basic Introduction to Quantum Entanglement

What is the most basic unit of information? The answer is illustrated in Longfellow's poem "The Midnight Ride of Paul Revere", in which Revere's friend is instructed to shine signal lanterns from the tower of Boston's North Church

   "One if by land, and two if by sea"

to alert the rebel defense forces of the direction of impending attack by the imperial enemy.

What Revere's friend is sending is a bit---the most basic unit of information. The bit in this poem represents a choice between the two possibilities "land" and "sea". More generally, a bit can represent any pair of choices: yes or no; on or off; buy or sell; or 0 or 1.

In the quantum world, the bit is replaced by the quantum bit as the basic unit of information. Where the bit must choose between 0 and 1, the quantum bit has an infinite number of in-between states called superpositions of 0 and 1. To explain by analogy with a coin, a bit must be either "heads" or "tails", but a quantum bit can be a little bit of both at the same time. Erwin Schrödinger, one of the early developers of quantum theory, expressed superposition in a famously stark form with an experiment in which his cat is in a state in-between "alive" and "dead".

Quantum information gets more interesting when more than one quantum bit is involved. It is a most remarkable fact that two quantum bits can exist in entangled states that contain more information than is possible with two unentangled quantum states. By contrast, two bits can only be in one of four possible states: 00, 01, 10 or 11. A two-bit state is completely specified by the one-bit states of its single-bit subsystems. An entangled state of a two-quantum-bit system, on the other hand, cannot be fully described by the states of its single-quantum-bit subsystems.

Quantum information science took a huge leap in 1994 when Peter Shor discovered that entangled states can be processed to solve problems that have no known solution using ordinary bits and computers. Using Shor's discovery, quantum computers will be able to crack today's state-of-the art data encryption. For example, when you send your credit card number to a retailer over the internet today, you can be very certain that your data is secure; once quantum computers have been built, the code protecting your credit card number can be quickly broken. Shor's insight woke up the scientific world to the computational possibilities and power of quantum entanglement.

Applications of entanglement in quantum information theory include: computation, such as Shor's algorithm; communication protocols, such as data encryption that cannot be broken without violating the laws of physics; and nanotechnology, such as ultrafine quantum measurement. These applications and more motivate a thriving international research community that involves physicists, mathematicians, computer scientists, and engineers.