The superposition, or quamtum-entanglement of two particles that once interacted is easy to achieve, but maintaining that superposition is very hard, for both particles must be isolated from external influences otherwise the superposition will be broken in a process called collapse of the wave-function. When it happens the collapse is instantaneous for both particles, but no information can be transmitted by forcing the wavefunction of one of a superpostional pair of particles to collapse, so no physical law is broken; nothing, not even information, can be transmitted at speeds in excess of that of light.
The number of permutations that n qu-bits can have, is equal to 2(n+1)-2, which is more than the equivalent digital binary computer can manage, being 2n. More than one pair of particles can exist in a Quantum Superposition of states. Thus if three particles are in a quantum superposition, then there are fourteen superpositional states, or degrees of freedom, that they encode, all three particles have these fourteen properties simultaneously. It is only when the wave-function collapses that the particles assume individual quantum states. These quantum superpositional states are called qu-bits, and can behave like a computer. 31 particles in a quantum superposition can have 2(31+1)-2 properties all at once, and as such, they can explore 2(31+1)-2 outcomes of an interaction simultaneously. Thus, computations that would take a conventional computer decades to explore the possible outcome of 4,294,967,294 states would take a quantum computer a fraction of a microsecond. Quantum computers would be immensely powerful beasts. The disadvantage is that not many problems can be arranged in such a way as to be solveable by quantum computer. Quantum computers are proving to be immensely difficult to make, so far (2003) a quantum computer with only two qu-bits has been made, which can perform just 2 calculations at once, not worthwhile at all. But with every unity increment in qu-bits, the power of a quantum computer doubles. A 31 qu-bit computer would be immensely powerful, possibly capable of solving the complicated folding of proteins. Another possible task for quantum computers is the factorisation of large numbers, larger than 2128, but a way has to be devised to parse the question in a way that a quantum computer can come up with a meaningful answer. [This is reminiscent of the question: What is the answer to Life, the Universe, and, well, Everything? Answer: 42]. Ideally, the military would like quantum computers to be for their sole purposes, and that no one else has access to one. To that end, the most advanced research on quantum computers is done by the military in secret, and they may well be up to a 12-qu-bit computer by now for all the plebeians know (though if they are - they don't display such superior intellect by their mundane actions). The quantum calculation is a bit like the way that soap films will almost instantly solve a minimal area problem, one that a conventional computer could take days to perform if the number of areas is large. The soap film solves the problem in a totally different way to that of a conventional computer, which solves a problem sequentially. Both the quantum computer and the soap film solve problems in parallel, all at once, almost as if they knew the answer already.
A fundamental upper limit to the power of any computer has just emerged from research into entropy. It appears that the Universe cannot contain a computer more powerful that one that has 10120bits, the calculation being based on the size of the visible Universe, the speed of light and Heisenbergs Uncertainty Principal where the amount of energy contained in a given volume of space is associated with a certain time period. It turns out that there is a limit to the amount of entropy that the Universe can contain; any more matter and that matter will spontaneously self-organise into entities with less entropy. This limits the maximum size of any computer to 10120bits. A quantum computer based on the entanglement of spins would reach this limit with only 400 entangled particles. This makes the idea at least testable in practice, but as yet, scientists are nowhere near making a quantum computer with that many entangled particles.
Other possible uses for quantum entanglement include tele-portation (the cloning of another object at a distance), high-resolution imaging, and quantum cryptography.
In fact I, Roger Darlington, think this quantum entanglement was instrumental in the formation of the Universe right at its very inception; the Big Bang. Here, all particles came from one source, and many, if not all, must have been entagngled together in one gigantic web of spooky connections. The timescale is extremely short, and there seems ample opportunity for quantum entanglement to have existed as the Universe expanded from a single point in space to 10-16cm, or even to a much larger size. Cosmologists tell us that there was no causal connection between expanding regions of space separated by more than a few degrees, because as the energy expanded and cooled, the space for the energy to fill also expanded, and this expansion occured faster than light. No law was broken, space can expand faster than light. But the cosmologists cannot fully explain how physically completely separate places that were receding from each other faster than the speed of light can yet possess more or less the same cosmic temperature as if it was in thermal equilibrium. [This temperature, extremely hot then, was to become the now observed cold cosmic microwave background radiation that is almost the same in every direction]. How could physically separate areas which were in another Universe invisible to the one we found ourselves in have been in thermal equilibrium? If the particles in physically separate areas were in quantum entanglement, that is how! The spooky action at a distance that operates faster than light-speed. That mechanism may offer a way for thermal equilibrium to occur over dis-connected parts of the Universe.
By using the number of particles in the Universe the total amount of information they could hold was calculated by Seth Lloyd of MIT at 1090 bits. The number of logical operations that could be performed on those bits is limited by the energy available to carry out those operations, the speed of light (which determines the speed at which information can move) and the running time (the age of the Universe). This works out at 10120 logic operations that could have been performed since the Big Bang.
In fact, I go even further than that! The myriads of particles that were the Big Bang, if they were in quantum entanglement, would form an immense quantum 'computer'; one that consisted of a myriad of qu-bits, one capable of the most un-imaginable calculations, whose very output was the form that the expanding Universe would take, the form that the particles would take, their properties, their quantum numbers, the seemingly random values that the fundamental constants have assumed, the very form that space and time itself would assume, the fabric of the Universe. This computer was the ultimate recursive computer, its own self-referral was complete; it decided on its own form, and as it expanded, the calculations changed determining its' next state. No computer on Earth could every perform such calculations of immense proportion, a computer the size of the Universe would be required in order to do so. Quantum entanglement is profound indeed. See below my letter to New Scientist expounding this theory which was written on the 18th June 1998, not long after quantum computers became a known possibility.
For publication in the 'Letters' of New Scientist Magazine:
In response to the articles "Anything Goes" and "Jim's Bright Idea" in New Scientist 6 June 1998, I contend that the ultimate quantum computer has already run, and that it ran about 10 billion years ago when all the matter was gathered together just after the Big Bang. Here, the swarm of particles quantumly interacted with each other creating a multitudinous soup of quantumly bound particle pairs. This mass of particles now all intimately knew each other and behaved as one evolving communion. Together this throng arrived, by pan-mutual consensus, at an answer mutually acceptable to all present, and this answer was the set of fundamental constants of nature and the Universe. Thus, the Universe itself decided upon it's own physical constants that were self-consistent with itself. The ultimate quantum computer, had, in an instant and by virtue of its myriad of interacting elements, solved the answer to Life, the Universe, and, well, Everything. Meanwhile, 10 billion years later, humans are still striving to fathom it all out.
R.W.Darlington, Manchester, England.
Physicists now (2004) think that quantum entaglement between a multitude of particles exists everywhere, all the time, and not just in their highly contrived experiments. This, of course, comes as no surprise to myself. Their effects may affect even the everyday macroscopic properties of materials, or be responsible for some of them. In a paramagnetic material, the spins of some of the materials' atoms (which imparts each atom with a magnetic field) align with an externally applied magnetic field. The magnitude of this effect is called the magnetic susceptibility of that material. It has been found that the magnetic susceptibility of a paramagnetic salt containing holmium atoms is greater at very low temperatures than should be the case, the quantum entanglement between the atoms being the only explanation for the extra magnetic susceptibility. The entanglement also affects the salts' heat capacity, the amount of heat required to raise its' temperature by a given amount.
Researchers believe entanglement affects the properties not only of paramagnetic salts, but causes significant effects in other materials, such as superconductors or superfluids. [Superconductors are in a Bose-Einsten Condensation state]. Quantum entanglement can also explain one of the defining properties of a superconcuctor - The Meissner effect, where a magnet levitates above a superconducting material. The magnet induces an electrical current within the surface of the superconductor, and this current produces an equal but opposite magnetic field that repels and suspends the magnet. No magnetic field is allowed to penetrate the superconductor. This effect can only be achieved if the electrons that generate the current within the superconductor are in an entangled state. The current halts the progression of the virtual photons associated with the magnetic field keeping them near the surface of the superconductor; it is as if the normally massless photons have suddenly entered treacle, slowing them down, and effectively endowing them with mass.
Something similar may explain the masses of the fundamental particles.
The fermions, electrons, neutrinos and quarks all possess mass. But the
particles that transmit the forces between these fermions, (the so-called
force carrying particles or
guage bosons as they are also known) like the photon (which conveys the
electro-magnetic force), the graviton (which conveys the gravitational
force), the W- and Z particles (which convey the weak force), and the
gluons (which convey the strong force) should all be massless and
therefore infinite in range. However, in reality, the latter two possess
mass and are therefore limited in range. It is believed that the source of
mass is the Higgs field, which permeates every corner of the Universe and
is mediated by a particle called the Higgs boson. Just like
superconductors, the Higgs bosons are thought to exist as a Bose-Einsten
condensate, where they are all in the same quantum state. And just the way
that entangled electrons in superconductors exclude the photons of the
magnetic field from their bulk, so too do the entangled Higgs particles of
the Higgs field exclude gluons and other guage bosons, giving them an
effective mass and also limiting their range of influeunce. Quantum
entanglement may be linked to not just the mass of the guage bosons, but
also to the mass of all fundamental particles, including the Higgs boson
itself. Different particles would react differently to the entangled Higgs
bosons, and would therefore be bestowed with differing effective masses,
which would sometimes be zero (photon).
See Higgs Boson
Even the virtual particle pairs created in a vacuum are probably in an entangled state. Some now believe that all interactions between particles generate entanglement. It has even been shown by a thought experiment that time itself can become entangled: measure the polarisation of a single photon twice in succession, and the second measurement can affect the earlier measurement! This is an inversion of cause and effect, putting time in the quantum world on an equal footing with space. (c.f. Space-Time in the macroscopic General Relativity context). Again, this just goes to further support my theory of the Big Bang outlined above. Perhaps the way that the collapse of entanglement seems to involve the otherwise inexplicable simultaneous resolution of the quantum state of both particles that may be separated by cosmological distances would be reconcilable if time were permitted to be able to somehow reverse as well. This should give a clue as to what may be happening. It is truly mind-boggling.