In collaboration with Danilo Zia and Fabio Sciarrino from
Sapienza University of Rome, researchers at the University of Ottawa recently
showcased a novel technique that makes it possible to visualise the wave
function of two entangled photons—the fundamental particles that make up
light—in real-time.
The idea of entanglement is comparable to picking a shoe at
random when compared to a pair of shoes. As soon as you recognise one shoe, you
can always tell what the other shoe is like—left or right—no matter where in
the cosmos it is. The interesting aspect, though, is the inherent uncertainty
surrounding the identification process up until the precise observational
moment.
A fundamental concept in quantum mechanics, the wave
function offers a thorough understanding of a particle's quantum state. For
example, in the shoe example, the shoe's "wave function" could carry
data about left or right, size, colour, and other attributes.
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| Biphoton state holographic reconstruction. Image reconstruction. a, Coincidence image of interference between a reference SPDC state and a state obtained by a pump beam with the shape of a Ying and Yang symbol (shown in the inset). The inset scale is the same as in the main plot. b, Reconstructed amplitude and phase structure of the image imprinted on the unknown pump. Credit: Nature Photonics |
To put it another way, the wave function lets quantum
scientists anticipate what will probably happen when they measure different
aspects of a quantum entity, like position, velocity, etc.
This ability to predict the future is extremely valuable,
particularly in the quickly developing field of quantum technology, where it is
possible to test the computer itself by understanding the quantum state that is
generated or input into a quantum computer. Furthermore, the incredibly complex
quantum states used in quantum computing involve numerous entities that may
show strong non-local correlations, or entanglement.
It is difficult to determine the wave function of such a
quantum system; this process is called quantum state tomography, or simply
quantum tomography. A complete tomography using the conventional methods (which
are based on the so-called projective operations) necessitates a high number of
measurements, which rises quickly as the system becomes more complex
(dimensionality).
The research group's earlier experiments using this method
demonstrated that it can take hours or even days to characterize or measure the
high-dimensional quantum state of two entangled photons. Furthermore, the
quality of the result is highly dependent on the complexity of the experimental
setup and is sensitive to noise.
One way to conceptualise the projective measurement approach
to quantum tomography is as viewing shadows of a high-dimensional object
projected from independent directions on various walls. A researcher can only
see shadows, but they can still deduce the shape and state of the entire object
from those shadows. For example, in a CT scan (computed tomography scan), a set
of 2D images can be used to reconstruct the information of a 3D object.
But there's another method in classical optics for
reconstructing a three-dimensional object. This technique, known as digital
holography, works by using a reference light to interfere with the light that
an object scatters in order to record a single image known as an interferogram.
The group expanded this idea to the case of two photons
under the direction of Ebrahim Karimi, associate professor in the Faculty of
Science, co-director of the uOttawa Nexus for Quantum Technologies (NexQT)
research institute, and holder of the Canada Research Chair in Structured
Quantum Waves.
In order to reconstruct a biphoton state, it must first be
superimposed over a presumed well-known quantum state, and the spatial
distribution of the positions at which two photons arrive simultaneously must
then be examined. A coincidence image is a picture taken of two photons
arriving at the same time. These photons could originate from the unidentified
source or the reference source. According to quantum mechanics, it is
impossible to pinpoint the photons' source.
As a result, an interference pattern is produced that can be
utilised to piece together the wave function that is unknown. An advanced
camera that captures events on individual pixels with nanosecond resolution
made this experiment possible.
One of the paper's co-authors, Dr. Alessio D'Errico, a
postdoctoral fellow at the University of Ottawa, emphasised the enormous
benefits of this novel strategy by saying, "This method is exponentially
faster than previous techniques, requiring only minutes or seconds instead of
days." Notably, the complexity of the system has no effect on the
detection time, which addresses the long-standing scalability issue in
projective tomography."
This research has an impact that extends beyond academia.
Improvements in quantum state characterization, quantum communication, and the
creation of novel quantum imaging methods could all benefit from its potential
to hasten the progress of quantum technology.
The study "Interferometric imaging of amplitude and
phase of spatial biphoton states" was published in Nature Photonics.