Quantum cryptography is one of the most promising quantum technologies of
our time: Exactly the same information is generated at two different
locations, and the laws of quantum physics guarantee that no third party can
intercept this information. This creates a code with which information can
be perfectly encrypted.

The team of Prof. Marcus Huber from the Atomic Institute of TU Wien
developed a new type of quantum cryptography protocol, which has now been
tested in practice in cooperation with Chinese research groups: While up to
now one normally used photons that can be in two different states, the
situation here is more complicated: Eight different paths can be taken by
each of the photons. As the team has now been able to show, this makes the
generation of the quantum cryptographic key faster and also significantly
more robust against interference. The results have now been published in the
scientific journal Physical Review Letters.

### Two states, two dimensions

"There are many different ways of using photons to transmit information,"
says Marcus Huber. "Often, experiments focus on their photons' polarization.
For example, whether they oscillate horizontally or vertically—or whether
they are in a quantum-mechanical superposition state in which, in a sense,
they assume both states simultaneously. Similar to how you can describe a
point on a two-dimensional plane with two coordinates, the state of the
photon can be represented as a point in a two-dimensional space."

But a photon can also carry information independently of the direction of
polarization. One can, for example, use the information about which path the
photon is currently traveling on. This is exactly what has now been
exploited: "A laser beam generates photon pairs in a special kind of
crystal. There are eight different points in the crystal where this can
happen," explains Marcus Huber. Depending on the point at which the photon
pair was created, each of the two photons can move along eight different
paths—or along several paths at the same time, which is also permitted
according to the laws of quantum theory.

These two photons can be directed to completely different places and
analyzed there. One of the eight possibilities is measured, completely at
random—but as the two photons are quantum-physically entangled, the same
result is always obtained at both places. Whoever is standing at the first
measuring device knows what another person is currently detecting at the
second measuring device—and no one else in the universe can get hold of this
information.

### Eight states, eight dimensions

"The fact that we use eight possible paths here, and not two different
polarization directions as it is usually the case, makes a big difference,"
says Marcus Huber. "The space of possible quantum states becomes much
larger. The photon can no longer be described by a point in two dimensions,
mathematically it now exists in eight dimensions."

This has several advantages: First, it allows more information to be
generated: At 8307 bits per second and over 2.5 bits per photon pair, a new
record has been set in entanglement-based quantum cryptography key
generation. And secondly, it can be shown that this makes the process less
susceptible to interference.

"With all quantum technologies, you have to deal with the problem of
decoherence," says Marcus Huber. "No quantum system can be perfectly
shielded from disturbances. But if it comes into contact with disturbances,
then it can lose its quantum properties very easily: The quantum
entanglements are destroyed." Higher-dimensional quantum states, however,
are less likely to lose their entanglement even in the presence of
disturbances.

Moreover, sophisticated quantum error-correction mechanisms can be used to
compensate for the influence of external perturbations. "In the experiments,
additional light was switched on in the laboratory to deliberately cause
disturbances—and the protocol still worked," says Marcus Huber. "But only if
we actually used eight different paths. We were able to show that with a
mere two-dimensional encoding a cryptographic key can no longer be generated
in this case."

In principle, it should be possible to improve the new, faster and more
reliable quantum cryptography protocol further by using additional degrees
of freedom or an even larger number of different paths. "However, this not
only increases the space of possible states, it also becomes increasingly
difficult at some point to read out the states correctly," says Marcus
Huber. "We seem to have found a good compromise here, at least within the
range of what is currently technically possible."

## Reference:

Xiao-Min Hu et al, Pathways for Entanglement-Based Quantum Communication in
the Face of High Noise, Physical Review Letters (2021).
DOI: 10.1103/PhysRevLett.127.110505

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