Together with Danilo Zia and Fabio Sciarrino from the Sapienza University
of Rome, researchers at the University of Ottawa recently showed a new way
to see the wave function of two entangled photons(photons are the basic
particles that make up light) in real time.

Drawing a comparison between tangling and picking a shoe at random is a
good way to explain it. As soon as you recognize one shoe, you can quickly
tell what the other is, including whether it is the left or right shoe, no
matter where it is in the world. But what's interesting is that the
identification process is inherently unclear until the exact moment of
discovery.

The wave function, which is one of the most important ideas in quantum
physics, tells us everything we need to know about a particle's quantum
state. In the case of the shoe, the "wave function" could carry information
like whether the shoe is left or right, its size, color, and so on.

To be more specific, the wave function lets quantum scientists guess what
will probably happen when they observe different things about a quantum
object, like its position, speed, etc.

This ability to predict the future is very useful, especially in the area
of quantum technology, which is developing very quickly. For example, if you
know the quantum state that is created or fed into a quantum computer, you
can test the computer itself. In addition, the quantum states used in
quantum computing are very complicated and include a lot of different things
that can have strong non-local connections (entanglement).

It is hard to figure out the wave function of a quantum system like this.
This is also called quantum state tomography, or just quantum tomography.
With the usual methods, which are based on what are called "projective
operations," a full tomography needs a lot of measurements, and the number
of measurements needed quickly goes up as the system gets more complicated
(dimensionality).

The study group has already done tests with this method that showed it can
take hours or even days to describe or measure the high-dimensional quantum
state of two photons that are linked. The quality of the answer is also very
sensitive to noise and relies on how complicated the experiment was set
up.

You can think of the projective measuring method for quantum tomography as
looking at the shadows of a three-dimensional object that are cast on
different walls from different directions. Researchers can only see the
shadows, but they can figure out what the full thing looks like by looking
at those shadows. A CT scan (computed tomography scan) is one example of how
the information of a 3D object can be put back together from a set of 2D
pictures.

But in classical optics, there is another way to put together a 3D shape.
This is known as digital holography, and it works by taking a single
picture, or interferogram, of the light that an item scatters and comparing
it to a reference light.

It was led by Ebrahim Karimi, who is a Canada Research Chair in Structured
Quantum Waves, co-director of the uOttawa Nexus for Quantum Technologies
(NexQT) research lab, and associate professor in the Faculty of Science. His
team took this idea and applied it to two photons.

To rebuild a biphoton state, you have to put it on top of a likely
well-known quantum state and then look at how the places where two photons
arrive at the same time are spread out in space. A chance image is a picture
of two photons arriving at the same time. They could come from the known
source or the reference source. According to quantum physics, it is not
possible to figure out where the photons come from.

This makes an interference pattern that can be used to figure out the wave
function that isn't known. This experiment was possible because of a
high-tech camera that catches events on each pixel with a precision of one
nanosecond.

Dr. Alessio D'Errico, a research fellow at the University of Ottawa and one
of the paper's co-authors, talked about how great this new method is: "This
method is exponentially faster than previous techniques, requiring only
minutes or seconds instead of days." It's important to note that the
complexity of the system doesn't change the detecting time. This solves the
long-standing problem of scale in projective tomography.

The effects of this study go beyond just the academic world. It might speed
up progress in quantum technology, like making it easier to describe quantum
states, communicate quantum information, and create new quantum image
methods.

The research paper called "Interferometric imaging of amplitude and phase
of spatial biphoton states" was released in the journal Nature
Photonics.