There has been an interesting debate on the quantum versus classical origin
of ghost imaging in thermal light. To clarify this quantum-classical
dilemma, Lixiang Chen at Xiamen University of China formulated a density
matrix to fully describe thermal two-photon orbital angular momentum state,
which revealed the hidden quantumness with non-zero discord. Then, a scheme
of mimicking teleportation was devised to demonstrate the possibility of
teleporting an optical image, with an accompanying featureless background.

In science fiction, "teleportation" is commonly portrayed as a means to
transfer physical objects from one location to another one some distance
away. But in physics, quantum teleportation only transfers quantum
information, i.e., the quantum state of a particle, without any physical
transmission of the particle itself. The quantum protocol of teleportation
was theoretically developed by Bennett and coworkers in 1993 and its first
experimental demonstration was realized by Bouwmeester and his colleagues in
1997. Recent progress has been made to realize the teleportation from a
transmitter on Earth to a receiver on a satellite, towards a global scale.
In the original scheme, quantum entanglement is an essential prerequisite
for implementing the teleportation.

On the other hand, ghost imaging represents an intriguing image acquisition
technique in which an image can be reconstructed by using a light beam that
never interacts with the object. However, it was demonstrated that, besides
quantum entangled biphoton source, classical thermal light source can also
be exploited for realizing the task of ghost imaging, thus raising a
question whether entanglement was truly necessary for ghost imaging. A lot
of distinguished work has contributed, both theoretically and
experimentally, however the quantum-classical dilemma still persists.

In a new paper published in Light Science & Application, Lixiang Chen
from the College of Physical Science and Technology, Xiamen University,
China, has investigated this on-going quantum-classical dilemma. In a photon
orbital angular momentum (OAM) Hilbert space, he formulated a density matrix
to fully describe two-photon state within a thermal light source, which
appears as a sum of a high-dimensional OAM entangled state and a diagonal
fully separable state. Interestingly, the density matrix is proven to be
separable, i.e., zero entanglement per se. Still, this formulation offers a
physically intuitive picture to reveal the quantumness hidden in thermal
two-photon OAM state, as was characterized by non-zero geometric discord
that discerns quantum correlations beyond entanglement.

A following question arises naturally as to whether such non-entangled yet
non-classical thermal two-photon state could be explored for any useful
quantum applications. The author answered this question positively by
revisiting the quantum teleportation protocol. The numerical simulations
showed that, at the single-photon level, the thermal two-photon OAM state
could be exploited for teleporting a high-dimensional OAM state, in which
the retrieved state is just a mixture of an exact replica of the original
state and a background maximally mixed one.

Unlike two-dimensional polarization state, the OAM eigenstates form an
infinite-dimensional, orthogonal, and complete basis. Therefore, a
complex-amplitude optical image can be equivalently represented by a
high-dimensional OAM state vector. Thus, the possibility of teleporting a
Clover image of both amplitude and phase modulation was also theoretically
demonstrated, with multiple repetitions of the protocol.

Professor Chen summarize the operational principle of the protocol like
this: "The light field, emitted from a thermal light source, is divided into
two paths by a non-polarizing beam splitter, which generates the thermal
two-photon OAM state. The photon in one path is directed to interact with
another third photon (encoded with the complex-amplitude Clover image) in
the high-dimensional Bell state measurement (BSM) stage. Conditional on the
BSM results and after being performed with a proper unitary operation, the
photon in the other path are sent to hit an ICCD camera working at the
trigger mode. Then, the original image can be retrieved correctly by the
ICCD camera, with multiple repetition of our protocol."

"In present proposal, the correct transmission of an image is ensured by the
pure high-dimensional OAM entanglement component, while the diagonal
completely mixed component merely brings about a featureless background." He
added.

"In the future, my theoretical framework can also call for further studies
of using thermal multi-photon state to demonstrate some new quantum
information tasks, such as remote state preparation and novel imaging with
undetected photons." Professor Chen forecasts.

## Reference:

Lixiang Chen, Quantum discord of thermal two-photon orbital angular momentum
state: mimicking teleportation to transmit an image, Light: Science &
Applications (2021).
DOI: 10.1038/s41377-021-00585-8

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