Entanglement:  The weirdest link

New Scientist vol 181 issue 2440 - 27 March 2004, page 32

That spooky connection between tiny particles is appearing everywhere, and its consequences are even affecting the world that we experience. It seems to unravel the past, and may be what keeps us alive. Quantum entanglement just got a whole lot weirder, says Michael Brooks

ENTANGLEMENT. Erwin Schrödinger called this phenomenon the defining trait of quantum theory. Einstein famously dubbed it spukhafte Fernwirkungen: "spooky action at a distance". It is not hard to understand why. Set things up correctly, and you can instantaneously affect the physical properties of a particle on the other side of the universe simply by prodding its entangled twin.

This is no longer just a curiosity of the quantum world, visible only in excruciatingly delicate experiments. Physicists now believe that entanglement between particles exists everywhere, all the time, and have recently found shocking evidence that it affects the wider, "macroscopic" world that we inhabit.

It is a discovery that might have far-reaching consequences. Not only will it give us a better grip on technological applications, such as quantum computing and cryptography, and the teleportation of quantum states, it could also open up a whole new realm of reality, enabling us to retain and control quantum weirdness in our everyday world. And it's not just a strange kind of "remote control" over matter that is at stake. Entanglement could even be the key to understanding what gives rise to the phenomenon of life. It's enough to set Einstein spinning in his grave.

Entanglement has been an affront to our sensibilities for several decades now. Schrödinger discovered it through his newly formed quantum theory, when he examined the mathematical descriptions of two quantum particles that bump into one other. After the interaction, it is impossible to tease apart the two particles' characteristics. Once they are entangled, it makes no sense to talk about the properties of just one of them. All the information about the particles, such as their momentum and spin, lies only in their joint properties. So if something affects the quantum state of one particle, it will inevitably affect the quantum state of the other, no matter how far apart they are. It is this that gives entanglement the "spooky" character that Einstein found so distasteful.

Although it seems like something from the realm of fantasy, many physicists now use entanglement as a kind of resource for experiments and applications. Entangled pairs of quantum particles such as photons are routinely created and sent down microscopes or fired across vast distances. Their spooky properties are used to perform such feats as high-resolution imaging, quantum teleportation or quantum cryptography.

But, despite the growing use of entanglement as a technological tool, physicists are beginning to realise we have only just scratched the surface of its potential. "Are there some other forms of entanglement that we haven't yet discovered?" asks Benni Reznik, a theoretical physicist at Tel Aviv University in Israel. "I think there are."

Just how little we know about entanglement was made crystal clear last year by a collaboration led by Sayantani Ghosh at the University of Chicago (Nature, vol 425, p 48). The team analysed experiments done more than a decade ago with a sample of a magnetic salt containing holmium atoms, and compared them with theoretical predictions. What they found is extraordinary.

The holmium atoms within the salt behave like tiny magnets and respond to each others' magnetic fields by adjusting their relative orientation, just as a compass needle orients itself to align with the Earth's magnetic field. But the atoms change this settled orientation if they are placed in an external magnetic field. The degree to which they align with the field is known as the salt's "magnetic susceptibility".

Ghosh and his colleagues examined how the susceptibility of the salt varied with temperature. They expected it would decrease as the temperature rose, because the extra energy at higher temperatures disrupts the atoms' ability to maintain the optimum alignment. And it did. But at very low temperatures, the atoms were aligned to a greater degree than would be expected if they had normal quantum energy levels (see Graphic). The team believe that quantum entanglement between the atoms is the only explanation for this phenomenon.

It's a big shock: it shows that the quantum phenomenon of entanglement, whose power was thought to be confined to the infinitesimal world of subatomic particles, can produce effects that remain measurable on macroscopic scales.

Ghosh and his colleagues also showed that entanglement affects the salt's heat capacity, defined as the amount of heat needed to change the temperature of a kilogram of substance by 1 kelvin. Throw in some heat, and you can only determine exactly how far the salt's temperature will rise if you take entanglement between atoms into account.

According to Vlatko Vedral, a theoretical physicist at Imperial College in London, these discoveries are highly important. Vedral was one of the team that first predicted the effect, three years ago (Physical Review Letters, vol 87, p 017901). The fact that the prediction has been borne out by experiment catapults the mystery of entanglement into the list of big unanswered questions that scientists need to address, he says.

That's partly because physicists can no longer content themselves with using the quantum and classical energy level descriptions of a material if they want to determine and understand its properties. The effects of entanglement now have to be included as an integral part of any accurate calculation.

But the results also suggest that, if we knew where to look, we might find entanglement causing significant effects in other materials. "It's not just magnetic salts - this should be a more universal thing," Vedral says.

The best place to look first, he believes, might be the enigmatic phenomenon of high-temperature superconductivity. Vedral points out that superconductors contain pairs of electrons whose quantum descriptions, or wave functions, appear to be entangled. "The wave function describing the pair is not equal to the product of two wave functions," he says. "Mathematically, I can see there is entanglement."

So should entanglement be considered as a possible cause of high-temperature superconductivity? Might it show us how to make materials that are superconducting at room temperature? At this stage, it is too early to say: the effects of entanglement on Ghosh's magnetic salt only become noticeable below 1 kelvin. "That is almost absolute zero," Vedral admits. "What would be really interesting would be to find a material that exhibits the effects of entanglement at higher temperatures." Eventually, he thinks, we might well find such a material at room temperature. "I don't think it's going to be a very easy search, but I can't think of anything that would rule this out on the basis of fundamental theory. It doesn't look impossible to me."

While this might seem hopelessly optimistic at first glance, other recent discoveries about entanglement are suggesting otherwise. Entanglements at room temperature appear to be an everyday part of the universe. Reznik, for instance, has shown that all of empty space - what physicists refer to as the vacuum - is filled with pairs of particles that are entangled. "It's an unusual idea," says Reznik. "It was quite hard to get our first paper on this accepted." His paper was finally published last year in Foundations of Physics (vol 33, p 167).

Thomas Durt of Vrije University in Brussels also believes entanglement is everywhere. He has recently shown, from the basic equations that Schrödinger considered, that almost all quantum interactions produce entanglement, whatever the conditions. "When you see light coming from a faraway star, the photon is almost certainly entangled with the atoms of the star and the atoms encountered along the way," he says. And the constant interactions between electrons in the atoms that make up your body are no exception. According to Durt, we are a mass of entanglements.

Curiouser and curiouser

Of course, that is no guarantee we can use them. Reznik says he doesn't think you can take his vacuum entanglement and use it to perform feats such as teleportation. Indeed, he is not even sure how to demonstrate that this entanglement exists. Though the equations of quantum field theory show that it is present, he is still working out how to perform an experiment that makes vacuum entanglement more than a theoretical result.

These are all tantalising revelations, because they suggest that something priceless is within our grasp. But how do we reach it?

We certainly need to find a better handle on practical entanglement: at the moment, the only forms of it we have learned to use are somewhat constraining. The entangled photons used for cryptography and teleportation are produced by firing a photon into a "non-linear" crystal, such as beta barium borate. The optical properties of a non-linear crystal depend on its orientation, and a photon fired in at the correct angle will split into two entangled photons. But the entanglement between the photon pair is an artefact of the internal properties of the original photon - its path and polarisation (New Scientist, 30 October 1999, p 32). So entangled photons from a non-linear crystal effectively remain just one quantum system, rather than being the result of two distinct particles meeting and interacting. "It's a kind of entanglement, but not quite the same as between different quantum systems," Vedral says.

What physicists would dearly like, the resource that would open the way for the best experiments, is an unlimited source of pure two-particle entanglements. Despite the recent progress, this rich source of quantum magic has eluded them so far. So how do we take things forward? Schrödinger first discovered entanglement through analysing the mathematical descriptions of quantum theory, so perhaps mathematicians should be the pioneers. The trouble with this is that entanglement gives mathematicians a severe headache - especially when the entanglement is between anything more than two particles.

In theory, just bouncing particles off an entangled pair will establish another entanglement link that can then be put to work, but it's much easier said than done. Experimental physicists John Rarity and Paul Tapster were the first to entangle three photons, in their laboratory at the UK Defence Evaluation and Research Agency in Malvern, Worcestershire, five years ago. But no one has ever managed to work out how to describe the properties of such a system. For the most part, theorists can't even look at a given quantum state and tell if it is entangled - it is only possible in a few special cases. "Although I can define what it means to be entangled, that is, I can write down a state that's entangled and a state that's not, if you give me a state and ask whether it's entangled, then I have no efficient way of telling you that," says Vedral. In other words, he knows how to formulate the calculation, but it is so difficult that no computer can actually perform it.

But these problems may be nothing compared to the bombshell that Caslav Brukner of the University of Vienna has just dropped. As if our current understanding of entanglement between widely separated particles were not sketchy enough, Brukner, working with Vedral and two other Imperial College researchers, has uncovered a radical twist. They have shown that moments of time can become entangled too (www.arxiv.org/abs/quant-ph/0402127).

They achieved this through a thought experiment that examines how quantum theory links successive measurements of a single quantum system. Measure a photon's polarisation, for example, and you will get a particular result. Do it again some time later, and you will get a second result. What Brukner and Vedral have found is a strange connection between the past and the future: the very act of measuring the photon polarisation a second time can affect how it was polarised earlier on. "It's really surprising," says Vedral.

This entanglement between moments in time is so bizarre that it could expose a hole in the very fabric of quantum theory, the researchers believe. The formulation does not allow messages to be sent back in time, but it still means that quantum mechanics seems to be bending the laws of cause and effect. On top of that, entanglement in time puts space and time on an equal footing in quantum theory, and that goes sharply against the grain.

Space and time have always been very different in quantum theory. A location in space is an "observable" - like momentum or spin, spatial coordinates are just another property any quantum particle can have. The passing of time, on the other hand, has always been part of the backdrop. An electron can have a particular value of spin, or momentum or location, but it cannot have a particular time.

But if time can become entangled, it should be considered as an observable, and there is no way to write that into quantum theory. "People have tried, but something in quantum mechanics always has to be violated if you want a proper time-observable," Vedral says. "So it could be that something in quantum mechanics has to be reformulated."

In other words, Brukner's result suggests that we might be missing something important in our understanding of how the world works. Maybe that shouldn't surprise us. After all, entanglement between two spatially separated objects already tells us that space doesn't really have the form that classical physics says it does: instantaneous cause and effect across cosmological distances is not something that any theory of the universe can cope with. And now Brukner's result seems to extend this "impossibility" to events separated in time as well.

It's not cause for despair, though. We know that relativity and quantum theory have to be meshed together if we are to create a "final" theory of how the universe works. It is too early to read much into Brukner's result, but maybe it is a clue about how to produce such a theory.

In the meantime, Vedral thinks he's identified an equally significant project to pursue. If, as Ghosh's result suggests, entanglement can produce macroscopic effects, is it such a stretch to reason that quantum entanglement might be the key to understanding life?

We know that quantum mechanics describes how atoms combine into molecules, and so underpins chemistry. And chemical processes underpin all biological processes, including the metabolic cycle and replication. So could entanglement support the emergent, macroscopic characteristic of chemistry that we call life? Reznik and Durt's revelations - that entanglements exist around us and inside us all the time - can only add to the intrigue. "I think it's a speculation worth making," Vedral says. "There may be some experiments in biology or biochemistry where we can see more of these effects, interpret some of the results in a different light. It would be a very exciting find."

Couple that with the ability to create materials that exploit our unfolding understanding of entanglement, and we might one day even gain the ability to use entanglement to create new forms of life. Now that is a spooky thought.