# 27 Dimensions! Physicists See Photons in New Light

Quantum computers and communications promise more powerful machines and unbreakable codes. But to make them work, it's necessary to measure the quantum state of particles such as photons or atoms. Quantum states are numbers that describe particle characteristics such as momentum or energy.

But measuring quantum states is difficult and time-consuming, because the very act of doing so changes them, and because the mathematics can be complex. Now, an international team says they found a more efficient way to do it, which could make it simpler to build quantum-mechanical technologies.

In a study detailed in the Jan. 20 issue of the journal Nature Communications, researchers from the University of Rochester and the University of Glasgow took a direct measurement of a photon's 27-dimensional quantum state. These dimensions are mathematical, not dimensions in space, and each one is a number that stores information. To understand a 27-dimensional quantum state, think about a line described in two dimensions. A line would have a direction in the X and Y coordinates — 3 inches left and 4 inches up, for instance. The quantum state has 27 such coordinates. [Quantum Physics: The Coolest Little Particles in Nature]

"We chose 27, kind of to make a point about 26 letters in the alphabet and throwing in one more," said Mehul Malik, now a postdoctoral researcher at theUniversity of Vienna. That means each quantum bit, or "qubit," could store a letter instead of a simple 1 or 0.

**Seeing a photon**

The group, led by Malik and Robert Boyd, a professor of optics and physics at the University of Rochester, was able to see a photon's states directly. They measured the photon's orbital angular momentum, which is how much the particles of light "twist" as they travel through space.

Ordinarily, finding the quantum state of a photon requires a two-step process. First, scientists have to measure some property of the photon, such as its polarization or momentum. The measurements are performed on many copies of the quantum state of a photon. But that process sometimes introduces errors. To get rid of the errors, the scientists have to look at what results they got that are "disallowed" states — ones that don't follow the laws of physics. But the only way to find them is to search through all the results and discard the ones that are impossible. That eats up a lot of computing time and effort. This process is called quantum tomography. [The 9 Biggest Unsolved Mysteries in Physics]

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A light wave is a combination of an electric and magnetic field, each of which oscillates and makes a wave. Each wave moves in time with the other, and they are perpendicular to each other. A beam of light is made up of lots of these waves.

Light can have what is called orbital angular momentum. In a beam with no orbital angular momentum, the peaks of the waves — the electric ones, for example — are lined up. A plane connecting these peaks will be flat. If the beam has orbital angular momentum, a plane connecting these peaks will make a spiral, helical pattern, because the light waves are offset from one another slightly as you go around the beam. To measure the state of the photons, scientists must "unravel" this helical shape of the waves in the beam.

**Measuring a photon's quantum state**

The team first fired a laser through a piece of transparent polymer that refracted the light, "unraveling" the helix formed by the waves. The light then passed through special lenses and into a grating that makes many copies of the beam. After passing through the grating, the light is spread out to form a wider beam.

After the beam is widened, it hits a device called a spatial light modulator. The modulator carries out the first measurement. The beam then reflects back in the same direction it came from and passes through a beam splitter. At that point, part of thebeam moves toward a slit, which makes a second measurement. [Twisted Physics: 7 Mind-Blowing Experiments]

One of the two measurements is called "weak" and the other "strong." By measuring two properties, the quantum state of the photons can be reconstructed without the lengthy error-correction calculations tomography requires.

In quantum computers, the quantum state of the particle is what stores the qubit. For instance, a qubit can be stored in the photon's polarization or its orbital-angular momentum, or both. Atoms can also store qubits, in their momenta or spins.

Current quantum computers have only a few bits in them. Malik noted that the record is 14 qubits, using ions. Most of the time, ions or photons will only have acouple of bits they can store, as the states will be two-dimensional. Physicists use two-dimensional systems because that is what they can manipulate — it would be very difficult to manipulate more than two dimensions, he said.

Direct measurement, as opposed to tomography, should make it easier to measure the states of particles (photons, in this case). That would mean it is simpler to add more dimensions — three, four or even — as in this experiment, 27 — and store more information.

Mark Hillery, a professor of physics at Hunter College in New York, was skeptical that direct measurement would prove necessarily better than current techniques. "There is a controversy about weak measurements — in particular, whether they really are useful or not," Hillery wrote in an email to LiveScience. "To me, the main issue here is whether the technique they are using is better (more efficient) than quantum-state tomography for reconstructing the quantum state, and in the conclusion, they say they don't really know."

Jeff Savail, a master's candidate researcher at Canada's Simon Fraser University, worked on a similar direct measurement problem in Boyd's lab, and his work was cited in Malik's study. In an email he said one of the more exciting implications is the "measurement problem." That is, in quantum mechanical systems the question of why some measurements spoil quantum states while others don't is a deeper philosophical question than it is about the quantum technologies themselves. "The direct measurement technique gives us a way to see right into the heart of the quantum state we're dealing with," he said. That doesn't mean it's not useful – far from it. "There may also be applications in imaging, as knowing the wave function of the image, rather than the square, can be quite useful."

Malik agreed that more experiments are needed, but he still thinks the advantages might be in the relative speed direct measurement offers. "Tomography reduces errors, but the post-processing [calculations] can take hours," he said.

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