IT IS the weirdest of the weird – Einstein certainly had no time for it. So how come quantum entanglement is being touted as the solution to some of humanity’s most pressing issues?
Entanglement is the bizarre phenomenon of quantum particles such as electrons remaining mysteriously linked, even when separated by enormous distances. Do something to one, and something happens to the other instantly, as if they weren’t really separate at all. Einstein doubted its existence, yet today physicists are putting it to work to build super-fast quantum computers and unbreakable quantum codes. And now researchers are considering a very strange use: pseudo-telepathy. That may sound frivolous, but it could have profound impact – helping humanity to solve age-old dilemmas.
For half a century, economists and evolutionary biologists have relied on “game theory” to make sense of a wide range of competitive situations, from ecosystems to international politics. The theory explores how competing individuals can plan their behaviour to achieve the most desirable outcome, and for most of its history, it has remained decidedly classical, based on the obvious idea that agents of any kind, from animals to nations, have to conform to the physical laws that govern the behaviour of large bodies like planets and people.
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But five years ago, physicist David Meyer of the University of California at San Diego began wondering what would happen to game theory in a quantum world. Not surprisingly, he discovered that things can get very strange, but in ways that may be profoundly useful.
In the quantum world, the impossible becomes the norm. Take the pion, for example, a subatomic particle that can decay into an electron and its antiparticle, a positron. When this happens – and it does so routinely – the two particles fly off in different directions. Yet they remain linked, quantum theory insists, even if they end up on opposite sides of the universe. Along with entanglement, another factor called superposition plays a part in this link.
Superposition describes the oddly indefinite character of a particle. Both electrons and positrons have a property called spin, which, when it is measured, is always either up or down. Prior to measurement however, the spin is considered to be in a superposition of both up and down. In a sense, quantum particles split their existence in a ghostly way. It is only upon measurement that the splitting collapses to yield particles with definite properties.
Entanglement stems from the fact that a superposition can involve more than one particle. In the case of our electron and positron, the electron’s spin is neither up nor down, and the same goes for the positron. The only definite characteristic is that the two spins oppose one another. Upon measurement, if you find the electron’s spin is up, then the positron’s spin will be down, and vice versa. Measure one, and as its spin becomes definite, the other is triggered to become definite as well. So quantum theory seems to imply that what happens in one part of the universe can have immediate effects in other parts, no matter how far away.
In the classical world of course, this is not possible. So how might a clever but classical individual put these quantum tricks to work in game theory? When Meyer first started exploring the subject, he discovered that quantum superposition allowed players to pull off some impressive stunts – and easily defeat those who used classical methods (żěè¶ĚĘÓƵ, 5 January 2002, p 12).
Magic squares
But it has now emerged that quantum strategies provide more subtle advantages than a mechanism for beating an unsuspecting opponent. The latest advances show quantum game theory can create seemingly impossible collaborations and render unworkable situations very workable indeed. That is because entanglement makes it possible for players to coordinate their actions and act as teammates without ever actually communicating. No wonder physicist Gilles Brassard of the University of Montreal in Quebec refers to the trick as pseudo-telepathy.
Two years ago, Padmanabhan Aravind, a physicist at the Worcester Polytechnic Institute in Massachusetts, invented what is perhaps the simplest example. In Aravind’s “magic squares” game – based on earlier work by physicist David Mermin at Cornell University, New York – two players named Alice and Bob play as teammates. The game goes as follows: two interrogators take the players to distant locations and ask each to choose a set of three numbers, either 0 or 1. Alice’s numbers will be placed into one of the rows of a grid of nine squares (see Graphic), and Bob’s numbers will be placed into one of the columns. Alice and Bob face three constraints. Alice has to make her numbers add up to an odd number (either 1 or 3), while Bob has to make his add up to an even number (0 or 2). To win the game, they also have to ensure that their two sets of numbers fit onto the same grid – that is, that the number at the intersection of Alice’s row and Bob’s column is the same.
According to classical physics, Alice and Bob cannot be sure of winning. If they cannot communicate, they face a mathematical contradiction. If asked to give numbers for rows or columns 1, 2 or 3, both players have to be prepared to spit out three numbers. So each has to have three sets of three numbers prepared in advance, numbers that would fill the grid of nine squares. Alice’s numbers, added up along the rows, have to add up to odd numbers, while Bob’s have to add up to even numbers. But that’s impossible. The sum of the sums of Alice’s three rows – an odd number – equals the sum of all the numbers in the box. But this is also the sum of sums for Bob’s three columns, which is an even number. No number is both odd and even, so Alice and Bob simply cannot plan a strategy to win.
Yet Aravind found that quantum theory offers Alice and Bob a miraculous solution. They don’t have to make their choices beforehand, and can use entangled particles to coordinate their answers even without communication. Before the experiment, they have to set up four quantum particles in a particular entangled state in which two have spin up and the other two have spin down. This state involves a superposition; which of the four particles are up and which are down is completely uncertain. Alice and Bob each send a pair of these particles to the places where they will make their decisions. When the time comes, Alice and Bob measure the spins of their two particles, obtaining two numbers each – a 1 for spin up and a 0 for down – and then choose a third 0 or 1 to make their three numbers add to an odd or even sum. Aravind proved that if Alice and Bob set up the initial state correctly, quantum connections ensure that they will always win the magic squares game – defying all classical possibilities.
“This is what we mean by pseudo-telepathy,” says Brassard. “It would appear as magical as true telepathy to a classical physicist, yet it has a perfectly scientific explanation: quantum mechanics.”
In a recent paper, Brassard, working with colleagues Anne Broadbent and Alain Tapp, compiled all the known games that would permit pseudo-telepathy. These games are of great interest to physicists because they highlight the differences between the classical and quantum worlds, and because studying them may help to clear up a lingering controversy: whether entanglement’s “spooky action at a distance” is indeed real, or whether there might still be some more classical and less bizarre explanation. “If implemented successfully,” says Tapp, “any one of these games would provide convincing evidence that classical physics does not rule the world.”
But the really exciting possibility opened up by pseudo-telepathy and other quantum effects lies in its support for an everyday human trait for social well-being: trust.
Take one of the most famous dilemmas in social theory: the problem of “free-riding” with public goods – enjoying things like clean air or national defence, whether or not you have helped to create them. Individuals face a temptation to cheat – to save energy or money by not contributing, while still enjoying the benefits. All too frequently, the outcome is social disaster.
This dilemma is hard to solve. One solution is a government with the power and authority to force individuals to contribute – through taxes, say. Another solution emerges if people play the game repeatedly and can punish cheaters for their behaviour. This makes cheating costly, and as economists showed in 2000, this carrot-and-stick approach enables a group to maintain a high level of contribution to public goods – to the benefit of all (American Economic Review, vol 90, p 980).
But quantum theory offers another solution, and one that does not require a painful learning process. Last year, physicist Tad Hogg and fellow Hewlett-Packard researchers Kay-Yut Chen and Raymond Beausoleil studied a game designed to represent the public-goods dilemma. In the game, a number of individuals choose how much to contribute to a public fund. The experimenter then multiplies the total value of their contributions by a certain factor – representing the benefit that accrues from investment in the public good – and redistributes the total back equally to the players. If all players contribute, the return on their investment is high and all do very well. But players have a strong incentive to cheat: a player can do even better if he does not contribute while everyone else does.
“Quantum entanglement lets people pre-commit to agreements”
In human experiments, players quickly succumb to the cheating temptation; they fail to contribute and the public fund dwindles to almost nothing. But quantum entanglement changes that. Hogg and his colleagues studied a situation in which the players share a set of entangled particles – one for each player – and use them in deciding whether to contribute or not. Each player chooses a strategy by manipulating the quantum state of his or her own particle, altering its state in a way that reflects their decision. After each person has “played” in this way, a measurement of all the particles then determines which players contribute and which cheat. Strategy enters because players can manipulate their particles so as to steer the ultimate measurement towards outcomes they would like.
The key difference in the quantum game lies in the links between particles. A change in the state of any one particle will instantly influence the state of the particles held by other players. Consequently, players automatically receive “tip-offs” about the willingness of others to cooperate, and on this basis can then adjust their own strategy. In effect, entanglement allows players to link their decisions together in a way that would not be possible classically. So it becomes likely that cheating by one person will automatically be met with cheating by others. In this way, cheating doesn’t pay, and quantum theory deters freeloading and promotes a better outcome. “Quantum entanglement allows individuals to pre-commit to agreements,” Hogg says. And as he and his colleagues have found, the “best” strategy in the quantum game, even for a completely selfish individual, leads to cooperation at least part of the time.
If this quantum game could be developed into a practical tool to help solve public-goods dilemmas, it could change the world. Perhaps the most pressing public-goods dilemma of our time is global climate change, which requires a commitment from all nations.
All nations have the incentive to “cheat” on global warming. After all, a cheating nation will get an economic leg-up while others scale back their emissions, yet also enjoy the improved health of the planet. The outcome, of course, may be quite the opposite: widespread cheating and a planet in increasing distress.
In principle, working with quantum theory could change that. If leaders were given a way to negotiate over climate change using quantum resources, they could cooperate more effectively. For now, this may be too much to hope for. As Hogg points out, global climate change is only partly a public-goods problem, because people also disagree over the costs and benefits of various outcomes, as well as on the potential for new technologies to emerge that would shift the character of the problem.
Far-reaching games
But other far-reaching applications may be possible – and even quite soon. The technical scheme for improving cooperation in the public-goods game only involves entanglement between pairs of quantum particles, which is easily possible with today’s technology. “This should allow physical implementation in the relatively near future,” Hogg says, in experimental form first, but perhaps in commercial settings soon after that. Businesses of all kinds face the free-rider problem, and a simple technical solution could save vast expenditure on legal costs. A quantum implementation of the game might automatically trigger the movement of funds from contributing firms into a central account for a joint venture, for example.
Of course, the weirdness of the quantum world could take some getting used to. Quantum game theory predicts good outcomes for these games, yet as Hogg points out, it is not clear whether people untrained in quantum theory, such as economic advisors, can learn to play them well. Along with Chen and Beausoleil, he has a series of experiments already under way to find out.
Throughout history, new technologies have led to sweeping changes in society – think of paper, the printing press and the computer. Quantum entanglement once seemed to be a remote theoretical obscurity, but perhaps it too could be the key to a better world.