One of the most mysterious features of quantum mechanics is that if two particles interact at some point in time then the properties of these particles will remain connected at future times. A consequence of this is that determining the quantum state of one of the particles simultaneously determines the quantum state of the other particle, even if the two particles are a long way apart. That quantum mechanics leads to this conclusion was first pointed out in a 1935 paper by Albert Einstein, Boris Podolsky, and Nathan Rosen, entitled Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? It involves a famous thought experiment known as the Einstein–Podolsky–Rosen experiment or, more commonly, the EPR experiment. This connectedness between particles was called entanglement by Erwin Schrödinger in a paper, also published in 1935, in which he emphasized that it is a key feature of quantum mechanics that distinguishes it from classical physics.
For many years quantum entanglement (sometimes known as quanglement) was a purely theoretical topic of interest mainly to people concerned with the philosophical foundations of quantum mechanics. This situation changed dramatically in 1964 when John Bell showed theoretically that experimental tests could be carried out to see whether the idea of quantum entanglement was correct (see Bell’s theorem). Experiments to investigate quantum entanglement were performed by Alain Aspect and his colleagues in the 1980s (see Aspect experiment). It is generally believed that these clearly and unambiguously showed that quantum entanglement is a real physical phenomenon.
The EPR experiment
The main point of the paper by Einstein, Podolsky, and Rosen was that it showed that the expectations of quantum mechanics are different to the classical view of physics, called local realism, in which a measurement at some point could have no effect on a measurement at a distant point at the same time. Since Einstein regarded quantum mechanics as an incomplete theory he expected that experiments would find that local realism would hold. A simplified version of the EPR experiment was put forward by the US physicist David Bohm (1917–92). An example of a system in which quantum entanglement can occur is given by the decay of a spin-zero particle into a pair of spin-½ particles, with one particle moving to the left while the other goes to the right. The spin of the particles, i.e. whether they have spin-up or spin-down, can be determined using the experimental set-up of the Stern–Gerlach experiment, with the important additional feature that the Stern–Gerlach detectors can both be rotated about the axis formed by the line along which the spin-½ particles move. The conservation of angular momentum means that if one of the particles is found to be spin-up then the other particle has to be spin-down. Once one of the particles is measured it is either definitely spin-up or spin-down, with the other particle automatically having to have the opposite spin, no matter how far away it is from the first particle.
Bell’s inequalities
In his remarkable paper of 1964, John Bell derived an expression, known as a Bell inequality, which gives the number of correlations in the results of two measuring devices on the basis of local realism. He then showed that quantum mechanics violates such inequalities, with there being more correlation in the results expected from local realism. When Alain Aspect and his colleagues tested Bell’s inequalities in the 1980s they used correlation experiments on the polarization of photons (rather than particle spin). They found clear evidence that Bell’s inequalities are violated in actual experiments, and hence that quantum mechanics is correct. After these experiments had been performed, some physicists were concerned that they implied that there is an instantaneous action at a distance interaction, and this would violate the special theory of relativity. However, subsequent careful investigation of this issue led to a result known as the ‘no communication theorem’, which states that no information can go from one detector to another detector faster than the speed of light, thus preserving the special theory of relativity.
It is possible to extend quantum entanglement to three or more particles. It was shown by Daniel Greenberger, Michael Horne, and Anton Zeilinger in 1987 that, whereas in two-particle entanglement the differences between local realism and quantum mechanics are statistical, with three or more particles the differences can sometimes be stated as certainties. It is possible for local realism to predict that a particle will certainly be spin-up whereas quantum mechanics predicts it will certainly be spin-down. Once again, experiments are firmly on the side of quantum mechanics being correct.
Loopholes have been thought up which might invalidate the conclusions of experiments on quantum entanglement but all such loopholes have been closed experimentally, albeit not so far by any experiment that could close all loopholes simultaneously.
Quantum computing
Quantum entanglement has been effected over distances of many kilometres and is an essential feature of certain emerging technologies such as quantum computing, quantum cryptography, and quantum teleportation. Quantum computing, in particular, has attracted considerable interest. The notion of two entangled states leads to the idea of a quantum bit or qubit, i.e. a superposed state that can store the bits 0 and 1 at the same time. A computer register made of three classical physical bits can store any of eight numbers, namely 000, 001, 010, 011, 100, 101, 110, and 111, but it can obviously store only one of these numbers at a time. A register made of three qubits could actually store all eight numbers simultaneously. The key point about a quantum register is that if it can be made to change to perform a computation, the processing occurs on all possible numbers in the register simultaneously. Also, increasing the number of qubits in the register increases the numbers exponentially. Four qubits store 16 numbers, five store 32, six store 64, and n cubits store 2n numbers. Consequently, a working quantum computer would have the potential for massive amounts of parallel processing. It is as if the computer were operating simultaneously in many parallel universes.
There are a number of problems with the idea of quantum computers, an obvious one being how to make one. Also there is a problem with the superposed states, which collapse to classical states by interacting with the environment – a process known as decoherence. More fundamentally, how would it be possible to access information? Measuring the state of a quantum register would simply collapse its wave function and give one of the eight possible numbers as in a classical register. Various quantum algorithms have been considered, aimed at using these quantum effects to give usable information based on probabilities. In 1994 interest in the subject increased considerably when Peter Shor of Bell Laboratories devised a quantum algorithm, Shor’s algorithm, that could, in principle, enable a quantum computer to factorize a large prime number. In 1996, Lov Grover designed Grover’s algorithm for sorting a database.