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. 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 entangle in both polarization and
angular momentum. “We wish to improve the quality of these hyperentangled
photons.”

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