Quantum Entanglement
One State for Two
Two Photons, One State
Shine violet laser light into a crystal of a certain kind, and now and then the crystal turns one violet photon into two infrared ones, each with half its energy. The two leave together and can be sent apart, each to a polarizing filter like the glass in sunglasses, with a detector behind it. A photon either passes its filter and makes the detector flash, or it is stopped.
Watch one side alone, and it looks like a coin toss. Half the photons pass and half are stopped, at random, whatever the angle of the filter.
Now set both filters at the same angle and compare the two sides. Whenever one photon passes, its partner passes too; whenever one is stopped, so is the other. Turn both filters to any other angle, still the same on both sides, and they still agree every time. That is the ideal; the best real sources agree well over 98 times in a hundred, the misses coming from imperfect parts. Distance makes no difference. A satellite has sent pairs down to two ground stations 1,203 kilometers apart, and the pattern survived the distance, blurred by the trip but clearly there.
This is entanglement. The pair has a definite state: the same answer at the same angle, whatever the angle. Neither photon has a state of its own. Ask what one photon’s polarization is, and the honest answer is that it has none; at every angle it answers like a coin. Everything there is to know is in the pair, and nothing is in either half. When the pair as a whole has a definite state, as here, the less one particle has a state of its own, the more strongly it is entangled with the other.
Albert Einstein found this hard to accept. He argued that the theory must be leaving something out, and called the effect spooky action at a distance. There is a plain way out, the one that works for gloves. Ship a pair of gloves in two boxes to two cities, and opening one box tells you at once what is in the other. Nothing spooky is going on: each glove was left or right from the start. Perhaps each photon, too, leaves the crystal carrying its answers. With one angle on both sides, no experiment can tell the two pictures apart.
Gloves, or Not?
For decades the question looked like philosophy. Then John Bell found a way to settle it, with more than one angle. A single photon at a single filter is easy to fake: answers carried in advance can match everything it does. Two photons far apart are another matter. Each is asked its question too far from the other for any news of it to arrive in time, unless something travels faster than light, and that is enough to catch ready answers out.
Bell’s argument can be told in a form anyone can follow. Give each filter three angles, a sixth of a turn apart. For each pair, set each filter to one of them at random, just before the photons arrive. Two facts come out. When the two filters happen to be at the same angle, the photons always agree, as before. When the angles differ, they agree only one time in four. That is the old rule of two filters in a row. Take either side first: when its photon passes, the other acts as if it had passed a filter at the same angle, and a filter turned a sixth of a turn from that lets through a quarter of the light.
Now try the gloves. Each photon would carry an answer for each of the three angles, pass or stop. Both would carry the same answers, which is why the same angles always agree. Take the three ways the filters can be set at different angles: the first and second, the first and third, the second and third. Three answers of only two kinds cannot all differ, so at least two of them are alike. On at least one of those three settings, then, the photons must agree. Whatever answers they carry, and however those change from pair to pair, photons with ready answers agree at least one time in three when the angles differ.
The measurement says one time in four. In the triangle’s terms it lights a quarter of each side, three quarters of one side in all, where any answers carried in advance light at least one whole side. That is below the floor, and no mix of answers can reach it, because the floor came from counting alone. So something must go. Either the photons do not carry answers for the angles they were never asked about, or something passes between the two sides faster than light, or the angles were never chosen freely but fixed in advance along with the answers. That is Bell’s theorem: no account with ready answers, no influence faster than light and freely chosen angles can match quantum physics.
Which one goes is still argued. The more common choice is to drop the ready answers. Views that drop them and still keep the speed-of-light limit pay elsewhere: either every result happens, each in a branch of its own, or the wave is only a tool for what to expect, not a real thing. The pilot-wave theory keeps results fixed in advance, by where the particles actually are. But what one photon does then depends, at once, on how the far filter is set, though no one can use that to send anything. No theory keeps both ready answers and the speed-of-light limit, unless the angles themselves were fixed in advance, an idea the tests below push far back in time.
Closing the Gaps
The first test used pairs of photons from calcium atoms, and its counts came out as quantum physics predicts. A later one switched the filters’ angles while the photons were in flight, though on a regular cycle that could be foreseen. Later still, each angle was picked at random in flight, so that no signal at the speed of light could tell one side what the other had chosen.
Two gaps stayed open for decades. If the two sides are too close, or set too slowly, a signal could still carry one side’s angle to the other in time. And detectors that catch only a small share of the photons might count an unfair sample. Then three experiments closed both gaps at once: one with two electrons in diamonds 1.3 kilometers apart, and two with photons. A fourth did it with two atoms 398 meters apart.
The test has also reached the circuits quantum computers are made of. Physicists put two superconducting chips 30 meters apart, joined by a tube cooled close to absolute zero, and ran the test more than a million times. The chance that answers carried in advance produced the result by luck came out below one in 10¹⁰⁸.
One assumption cannot be closed, even in principle: that each side’s angle is picked freely, and not fixed in advance by some cause in the shared past of the source and both switches. It can only be pushed back in time. In one test, about a hundred thousand people chose the angles for labs around the world by playing an online game. In another, the angles were chosen by light from two quasars, the blazing cores of distant galaxies, which left them 7.8 and 12.2 billion years ago. Any plan to arrange the result would have had to be laid before the Earth existed. That rules it out from 96 percent of the stretch of space and time in the experiment’s past.
Three photons make the clash sharper. Entangle three, give each filter two ways to be set, and quantum physics makes some results certain, not just likely: for three particular choices of settings, the three answers always come out in a fixed pattern. Answers carried in advance that keep all three patterns are forced to give one result for a fourth choice, and quantum physics predicts the opposite, every time. In the lab the three patterns held about 85 times in a hundred, so ready answers could give the quantum result in the fourth no more than about 45 times in a hundred. The photons gave it about 85 times. Run again with the three detectors far apart, and each setting picked at random too late for any signal at light speed to link them, the test came out the same.
No Message Rides on It
Measuring one photon seems to settle what its partner will do, and that looks like a way to send a message faster than light. It is not. Someone watching one side sees a coin toss whatever is done on the other side: measuring there or not, at any angle. The pattern appears only when the two lists of results are put side by side. The lists have to be brought together by ordinary means, no faster than light. Quantum theory itself proves that this holds for every measurement there could be, not just the ones tried so far. Nor can one side copy its photon many times over to peek at it: an unknown quantum state cannot be copied, and that has been proved too.
That is also why no one can say which side measured first and caused the other’s result. For two events far enough apart, observers moving in different ways disagree about which came first. If a message could ride on the pattern, some observers would see it arrive before it was sent. Since no message is sent, the results come out the same whichever side is taken to be first.
What a pair gives instead is a shared secret. Two sides that measure their photons at the same angles end up with the same string of random results, which the photons did not carry with them. A spy could try to catch each photon on the way, measure it and send on a new one with the same answer. That works only if the spy knows the angle each side will use. So the two sides switch among several angles at random, and afterwards compare a sample of their results in the open. Bell’s count on that sample is the alarm. The further the photons beat the floor that ready answers set, the less anyone else can share in their pattern, because a photon fully entangled with its partner can be entangled with nothing else. At the quantum limit, no one else can share it at all. Short of it, the two sides shorten their key until whatever a spy could know is wiped out. The same satellite has given two stations 1,120 kilometers apart a secret key from its pairs, and the pairs there beat the floor. A key has also been made whose safety rests on Bell’s test alone, without trusting the devices that made it.
Not a Thread
The picture most people carry is a thread between the two photons, tugged at one end and felt at the other. Two facts take it apart. The first is the one that keeps the key secret. Threads can be tied freely, one particle to a second, a third and a fourth. Entanglement cannot. A particle fully entangled with one partner can be entangled with nothing else at all, and one entangled a little with two partners shares out what it has. The sharing has a strict limit: what a particle shares with each partner, added up, can never exceed what it has. That is how a limited quantity behaves, not how a link behaves when it is tied.
The second fact removes the thread’s two ends. Start with two pairs made apart, photons 1 and 2 from one, 3 and 4 from the other. Measure photons 2 and 3 together, in a way that asks only which joint state the two are in and nothing about either alone. Photons 1 and 4, which have never met, come out entangled. This is called entanglement swapping. A half mirror can make such a measurement. Two photons exactly alike always leave it together; when photons 2 and 3 leave it by different ways, which happens one time in four, that alone says their polarizations are opposite at every angle, and says nothing about what either one is.
In one experiment the two pairs were made at different times, from one crystal. Photon 1 was caught at once, which destroyed it. Photon 2 was sent on a detour 31.6 meters long, which held it back 105 billionths of a second, the time between eight pulses of the laser. Meanwhile a later pulse made photons 3 and 4. Photon 2 came off the detour and was measured together with photon 3, and photon 4 was caught last.
Photons 1 and 4 came out entangled. Rebuilt from the records, their joint state matched an entangled pair to 77 percent, where no pair without entanglement can pass 50. Yet photon 1 was gone before photon 4 existed. A thread needs two ends at one time, and at no instant of this experiment were both of them in the world.
The experimenters also checked that the link was made in the middle and was not there all along. When photons 2 and 3 arrived far enough apart to be told apart, the joint measurement was spoiled, and photons 1 and 4 showed only an ordinary correlation, with no entanglement.
Nothing reached back to photon 1, either. A full joint measurement can give four results, and each leaves photons 1 and 4 in a different entangled state. In one the two always agree at the same angle; in another they always disagree; in the other two they agree at some angles and disagree at others. Take all the runs together, and the agreements and the disagreements cancel: the records of photons 1 and 4 show nothing at all. Sort them by the result in the middle, and each group shows an entangled pair. Photon 1’s record was written down and never changed; the label saying which group it belongs to came later, by ordinary means. Another experiment went further: whether photons 2 and 3 were measured together or one at a time was decided only after photons 1 and 4 had been measured. Here the entanglement shows up only as a relation between records, like two entries in a ledger that add up though they were written on different days.
Swapping is now the working part of quantum networks. Each end of a link is first entangled with a photon, the photons are measured together at a station in between, and the two ends come out entangled. The test with electrons in diamonds entangled its two electrons this way, and the same group has since linked electrons in two cities through 25 kilometers of fiber, with a station between them.
The same step can move a state, which is called teleportation. A photon measured together with one half of an entangled pair leaves the other half in one of four states, one for each result. Only when the result is sent on, by ordinary means, can the far side turn its photon to match, and then that photon carries the first one’s state. Photons’ states have been teleported from the ground to the satellite in orbit, as far as 1,400 kilometers, with the turn applied to the records afterwards. The full step, with the far photon turned in time, has been done across 143 kilometers between two islands.
Everywhere, Mostly Unseen
Entanglement is usually shown as a delicate effect coaxed out in a lab. It is closer to the rule. Among all the definite states two things could share, those that split into two separate halves are a vanishing sliver: pick one at random and it is entangled. When two things interact, they almost always become entangled. In some magnetic salts, the magnets of neighboring atoms pair up so that neither has a direction of its own. Cooled to a few degrees above absolute zero, such a salt answers a magnetic field in a way that can be explained only with its atoms’ magnets entangled. And the Large Hadron Collider has found top quarks and their antiquarks born entangled, though each lives less than a trillionth of a trillionth of a second.
Why, then, does it look so rare? Because nothing stays entangled with only one partner. Air molecules and stray light bump into everything, and each bump entangles a little more of the world with it. The pattern is still there, but spread over countless records that no one can gather back, so that each piece alone looks ordinary. This leaking away, called decoherence, is what hides the superpositions of large, warm things. The hard part is not making an entangled state. It is keeping one to two particles long enough to look at.
A quantum computer is a machine for doing exactly that. It entangles many qubits on purpose and steers them so that wrong answers cancel. Its builders’ main enemy is the room around it, which entangles itself with the qubits and spreads their pattern into the walls.
Stranger, but Only So Far
One last count turns the usual moral around. With answers carried in advance, filters at different angles agree at least one time in three. Entangled photons agree one time in four. Could some other quantum state, measured in some other way, agree even less, and still agree every time the angles match? No. Under that condition quantum physics cannot push the agreement below one in four in this test, whatever the pair and however it is measured. The limit has a general form that reaches beyond this one test.
Yet nothing in logic or relativity forbids going further. An imagined device could make the photons agree every time the angles match and never when they differ, and still send no message, since each side alone would see a coin toss, as now. So why does nature not do that? It stops at one in four: stranger than any answers carried in advance allow, and tamer than it had to be.
Why it stops there is still an open question, with candidate answers. Several proposed principles rule out the strongest imagined devices. One, called information causality, says that a single bit sent from one side can never let the other side read more than one bit of a list it has not seen, however many entangled pairs the two share. It gives exactly the quantum limit in the test most experiments use, with two angles a side, where ready answers score at most 2, entangled pairs 2.83 and the imagined devices 4. None yet singles out quantum physics in every case. A principle that did would say why the world is entangled just this much and no more.
