QUANTUM PARLOR TRICKS
Reality doesn’t exist until you measure it, quantum parlor trick confirms
by Adrian Cho / 20 July 2022
“The Moon isn’t necessarily there if you don’t look at it. So says quantum mechanics, which states that what exists depends on what you measure. Proving reality is like that usually involves the comparison of arcane probabilities, but physicists in China have made the point in a clearer way. They performed a matching game in which two players leverage quantum effects to win every time—which they can’t if measurements merely reveal reality as it already exists. “To my knowledge this is the simplest [scenario] in which this happens,” says Adan Cabello, a theoretical physicist at the University of Seville who spelled out the game in 2001.
Such quantum pseudotelepathy depends on correlations among particles that only exist in the quantum realm, says Anne Broadbent, a quantum information scientist at the University of Ottawa. “We’re observing something that has no classical equivalent.” A quantum particle can exist in two mutually exclusive conditions at once. For example, a photon can be polarized so that the electric field in it wriggles vertically, horizontally, or both ways at the same time—at least until it’s measured. The two-way state then collapses randomly to either vertical or horizontal.
Crucially, no matter how the two-way state collapses, an observer can’t assume the measurement merely reveals how the photon was already polarized. The polarization emerges only with the measurement. That last bit rankled Albert Einstein, who thought something like a photon’s polarization should have a value independent of whether it is measured. He suggested particles might carry “hidden variables” that determine how a two-way state will collapse. However, in 1964, British theorist John Bell found a way to prove experimentally that such hidden variables cannot exist by exploiting a phenomenon known as entanglement.
Two photons can be entangled so that each is in an uncertain both-ways state, but their polarizations are correlated so that if one is horizontal the other must be vertical and vice versa. Probing entanglement is tricky. To do so, Alice and Bob must each have a measuring apparatus. Those devices can be oriented independently, so Alice can test whether her photon is polarized horizontally or vertically, while Bob can cant his detector by an angle. The relative orientation of the detectors affects how much their measurements are correlated.
Bell envisioned Alice and Bob orienting their detectors randomly over many measurements and then comparing the results. If hidden variables determine a photon’s polarization, the correlations between Alice’s and Bob’s measurements can be only so strong. But, he argued, quantum theory allows them to be stronger. Many experiments have seen those stronger correlations and ruled out hidden variables, albeit only statistically over many trials. Now, Xi-Lin Wang and Hui-Tian Wang, physicists at Nanjing University, and colleagues have made the point more clearly through the Mermin-Peres game.
In each round of the game, Alice and Bob share not one, but two pairs of entangled photons on which to make any measurements they like. Each player also has a three-by-three grid and fills each square in it with a 1 or a –1 depending on the result of those measurements. In each round, a referee randomly selects one of Alice’s rows and one of Bob’s columns, which overlap in one square. If Alice and Bob have the same number in that square, they win the round. Sounds easy: Alice and Bob put 1 in every square to guarantee a win.
Not so fast. Additional “parity” rules require that all the entries across Alice’s row must multiply to 1 and those down Bob’s column must multiply to –1. If hidden variables predetermine the results of the measurements, Alice and Bob can’t win every round. Each possible set of values for the hidden variables effectively specifies a grid already filled out with –1s and 1s. The results of the actual measurements just tell Alice which one to pick. The same goes for Bob. But, as is easily shown with pencil and paper, no single grid can satisfy both Alice’s and Bob’s parity rules. So, their grids must disagree in at least one square, and on average, they can win at most eight out of nine rounds. Quantum mechanics lets them win every time.
“Summary of results. The winning probability for each query pair (x,y) is calculated from experimental data. The standard deviation is less than 0.01%, which is negligible in the histogram. The dotted blue line represents the unbiased classical bound 8/9.”
To do that, they must use a set of measurements devised in 1990 by David Mermin, a theorist at Cornell University, and Asher Peres, a onetime theorist at the Israel Institute of Technology. Alice makes the measurements associated with the squares in the row specified by the referee, and Bob, those for the squares in the specified column. Entanglement guarantees they agree on the number in the key square and that their measurements also obey the parity rules. The whole scheme works because the values emerge only as the measurements are made. The rest of the grid is irrelevant, as values don’t exist for measurements that Alice and Bob never make. Generating two pairs of entangled photons simultaneously is impractical, Xi-Lin Wang says.
So instead, the experimenters used a single pair of photons that are entangled two ways—through polarization and so-called orbital angular momentum, which determines whether a wavelike photon corkscrews to the right or to the left. The experiment isn’t perfect, but Alice and Bob won 93.84% of 1,075,930 rounds, exceeding the 88.89% maximum with hidden variables, the team reports in a study in press at Physical Review Letters. Others have demonstrated the same physics, Cabello says, but Xi-Lin Wang and colleagues “use exactly the language of the game, which is nice.” The demonstration could have practical applications, he says.
Broadbent has a real-world use in mind: verifying the work of a quantum computer. That task is essential but difficult because a quantum computer is supposed to do things an ordinary computer cannot. However, Broadbent says, if the game were woven into a program, monitoring it could confirm that the quantum computer is manipulating entangled states as it should. Xi-Lin Wang says the experiment was meant mainly to show the potential of the team’s own favorite technology—photons entangled in both polarization and angular momentum. “We wish to improve the quality of these hyperentangled photons.”
Researchers Use Quantum ‘Telepathy’ to Win an ‘Impossible’ Game
by Philip Ball / October 25, 2022
“To win at the card game of bridge, which is played between two sets of partners, one player must somehow signal to their teammate the strength of the hand they hold. Telepathy would come in handy here. But telepathy isn’t real, right? For decades, physicists have suspected that if bridge were played using cards governed by the rules of quantum mechanics, something that looks uncannily like telepathy should be possible. Now researchers in China have experimentally demonstrated this so-called quantum pseudotelepathy—not in quantum bridge but in a two-player quantum competition called the Mermin-Peres magic square (MPMS) game, where winning requires that the players coordinate their actions without exchanging information with each other.
Used judiciously, quantum pseudotelepathy allows the players to win each and every round of the game—a flawless performance that would otherwise be impossible. The experiment, conducted using laser photons, probes the limits of what quantum mechanics permits in allowing information to be shared between particles. The work “is a beautiful and simple direct implementation of the Mermin-Peres magic square game,” says Arul Lakshminarayan of the Indian Institute of Technology Madras, who was not involved in the experimental demonstration. Its beauty, he adds, comes in part from its elegance in confirming that a quantum system’s state is not well defined prior to actual measurement—something often considered to be quantum mechanics’ most perplexing trait. “These quantum games seriously undermine our common notion of objects having preexisting properties that are revealed by observations,” he says.
Two quantum physicists, Asher Peres and David Mermin, independently devised the MPMS in 1990. It involves two players (called Alice and Bob, as is tradition in quantum-mechanical thought experiments) who have to fill in a “magic square”—a three-by-three grid of numbers—with each grid element being assigned the value +1 or –1. In each round, a referee (Charlie) sends at random a row to Alice and subsequently a column to Bob (there are nine such row-and-column combinations). The players have to tell Charlie which values of +1 or –1 to put in their three grid spaces. As with any magic-square challenge (such as Sudoku), the sums of each row and column must meet particular constraints: here the product of all the entries in a row must equal +1, and the product of all the columns must be –1. Alice and Bob win a round if they both assign the same value to the grid element where the column and row overlap.
Classically it’s impossible to win all rounds because even if Alice and Bob guess well each time, there is inevitably one round for every completed square where their assignations must conflict. The best they can do is to achieve eight wins out of every nine. But now suppose that Alice and Bob can use this quantum strategy: Instead of assigning each grid element a value of +1 or –1, they assign it a pair of quantum bits (qubits), each of which has a value of +1 or –1 when measured. The value given by each player to a particular grid element is determined by measuring the two qubit values and finding the product of the pair. Now the classical conflict can be avoided because Alice and Bob can elicit different values from the same two qubits depending on how they make their measurements.
There is a particular measurement strategy that will ensure the winning criteria for any given round—that the products of Alice’s and Bob’s three entries are +1 and –1, respectively—are met for all nine permutations of rows and columns. There’s a wrinkle to this strategy, however. To make the right set of measurements, Alice and Bob need to know which of their three grid elements is the one that overlaps with the other player—they need to coordinate. But in the MPMS, this is no problem because they make their measurements sequentially on the same three qubit pairs. This means that the pair that reaches Bob has an imprint of how Alice has already measured those quibits: they can transmit information to each other.
In 1993 Mermin showed that the MPMS could be used to demonstrate a quantum phenomenon called contextuality. First identified by the Northern Irish physicist John Stewart Bell in 1966, contextuality refers to the fact that the outcome of a quantum measurement may depend on how the measurement is done. A set of classical measurements in a system will give the same results no matter what sequence those measurements are performed in. But for quantum measurements, this is not always so. In the MPMS, the contextuality arises from the fact that the measurement for a given qubit pair may give a different result depending on which other two pairs are being measured, too.
But what if we forbid any communication in the MPMS by assigning Alice and Bob different qubit pairs and saying that they can’t confer about how to measure them? Then each player can only be guaranteed nine out of nine wins if they make the right guesses about what the other player does. But in a study published in 2005, quantum theorist Gilles Brassard of the University of Montreal and his colleagues showed that the players can use quantum principles to guarantee a win in every round even without communicating by using what they called quantum pseudotelepathy. This strategy involves entangling one of each of the two qubit pairs sent to Alice or Bob with a corresponding qubit used by the other player.
Entangled particles have properties that are correlated, so if Alice measures the value for her particle, this fixes the value for Bob’s particle, too. Two entangled qubit particles could be anticorrelated, for example: if Alice’s qubit is found to have the value +1, Bob’s must be –1. There is no way of saying which value Alice’s qubit has before it is measured—it could be +1 or –1—but Bob’s will always be the opposite. Importantly, a property entangled between pairs of particles is said to be “nonlocal,” meaning that it is not “local” to either particle but rather shared between both. Even if the particles are separated by vast distances, the entangled pair must be regarded as a single, nonlocal object.
The same basic idea for winning a quantum game was proposed in 2001 by quantum theorist Adán Cabello of the University of Seville in Spain in a game he called “all or nothing,” which was later shown to be equivalent to the nonlocal (pseudotelepathic) MPMS. Some researchers regard entanglement as the most fundamental aspect of quantum mechanics. It implies a kind of information sharing between particles. That’s the key to leveraging entanglement for quantum pseudotelepathy: Alice and Bob don’t have to exchange information to coordinate their actions because the necessary information is already shared in the pairs of particles themselves. Both contextuality and nonlocality provide “quantum resources” that can be used to gain some advantage over classical approaches to information processing.
In quantum computing, for example, entanglement between the quantum bits is generally the resource that creates a shortcut to finding a solution to the problem unavailable to a classical computer. Physicists have repeatedly demonstrated Cabello’s all-or-nothing game in the real world using entangled photons. But while those experiments established how entanglement could convey a “quantum advantage” by beating classical performance, Kai Chen of the University of Science and Technology of China, Xi-Lin Wang of Nanjing University in China and their colleagues have devised a new experiment that they say implements the full protocol to achieve a guaranteed win in every round—genuine, consistent quantum pseudotelepathy.
Ideally Alice and Bob would prepare many sets of four qubits before the game starts, each quartet consisting of two entangled pairs. Alice would get one of each of these pairs, and Bob would receive the other. Making two entangled pairs of photons for each round of the game is immensely challenging, however, the researchers say. For one thing, the production of even a single entangled pair happens only with low probability in their apparatus, so making two at once would be extremely unlikely. And detecting two pairs at once, as the pseudotelepathic MPMS demands, is more or less impossible for this optical implementation. Instead Chen, Wang and their colleagues prepared single-photon pairs and entangled two of their properties independently: their polarization state and a property called orbital angular momentum. The photons were contained in ultrashort laser pulses lasting just just 150 femtoseconds and were entangled by passing them through two so-called nonlinear optical crystals.
A thin slab of barium borate first split a single photon into two of photons lower energy with correlated angular momenta. They were then entangled via their polarization, too, by sending them through a crystal of a yttrium-vanadium compound. To demonstrate a nearly 100 percent success rate, the researchers needed to improve their detection efficiency so that almost none of the entangled photons escape unseen. Even then the theoretical limit can’t be reached precisely in the experiment—but the researchers were able to show they could win every round with between 91.5 and 97 percent probability. This translates to reliably beating the classical eight-out-of-nine limit in 1,009,610 rounds out of a total of 1,075,930 played.
The pseudotelepathic MPMS game exploits the strongest degree of correlation between particles that quantum mechanics can possibly provide, Chen says. “Our experiment probes how to generate extreme quantum correlations between particles,” he says. If these correlations were any stronger, they would imply faster-than-light information exchange that a host of other independent experiments indicate is impossible. Mermin says that while experimentally impressive, this success reveals nothing new beyond the fact that quantum mechanics works as we thought. Cabello does not entirely agree. Above and beyond being an experimental tour de force, he says, the work shows a new wrinkle in what quantum rules make possible by mobilizing two sources of quantum advantage at the same time: one linked to nonlocality and the other linked to contextuality.
Investigating the two effects simultaneously, Cabello says, should allow physicists to more rigorously explore the connections between them. What’s more, each of these resources could in principle be put to different uses in quantum processing, boosting its versatility. “For example, nonlocality can be used for secret communication [using quantum cryptography] while contextuality can be used for quantum computation,” Cabello says. In this scenario, Bob could, for instance, set up secure communication with Alice while at the same time performing a computation with Charlie faster than classical methods permit.
The use of shared entanglement in these experiments “leads to effects that seem classically magical,” Lakshminarayan says. But given how often quantum mechanics is misused as a bogus justification for pseudoscientific claims, is it perhaps asking for trouble to call the phenomenon “pseudotelepathy”? It is “a bad term, inviting nonsensical interpretations,” Mermin says. But while Cabello agrees, he recognizes that evocative names can help to advertise the interest of the phenomenon. “Let’s not kid ourselves,” he says. “It is probably thanks to the word pseudotelepathy that [you and I] are having this conversation.”
MULTI SCALE ENTANGLEMENT
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