That Twist that Entangles All

cryptography holography inés urdaneta orbital angular momentum quantum entanglement Nov 06, 2023

Source of image here.

In a study published in Physical Review Letters [1], researchers report that entangled photons traveling in corkscrew paths have resulted in holograms that offer the possibility of dense and ultrasecure data encryption.

By Dr. Inés Urdaneta, Physicist at The International Space Federation

Commonly, there are two ways of having light carry information: through its polarization and through its angular momentum, in particular its orbital angular momentum (OAM).

The polarization concerns the geometrical orientation of light’s electromagnetic wave oscillations (of the electric and magnetic components of light). As explained in our former RSF article The origin of quantum mechanics I: The Electromagnetic field as a wave, an electromagnetic wave consists of a coupled oscillating electric field and magnetic field which are always perpendicular to each other. By convention, the polarization of electromagnetic waves refers to the direction of the electric field. In linear polarization, the fields oscillate in a single direction. Circular or elliptical polarization, like the one depicted in the animated image below, have the fields rotate at a constant rate in a plane as the wave travels, either in the right-hand or in the left-hand direction.

Circularly polarized light propagation showing the electric and magnetic components (the red and green 2D waves, respectively). Source of image here 

Common sources of EM radiation such as the sun or lamps radiate all sort of polarization and therefore, their net behavior is considered non-polarized. Polarized light can be produced by passing this unpolarized light through a polarizer (for example a slit), that allows waves of only one polarization to pass through it. Some materials like those exhibiting birefringence, dichroism, or optical activity, affect light differently depending on its polarization. And all chiral molecules -molecules that can’t be superposed with their mirror image- can do the same.  

Just like the hands, which are mirror image of each other, chiral molecules can't be superposed into a same image. 

According to quantum mechanics, electromagnetic waves are composed of a stream of particles called photons (read more on the quantization of light here). Viewed this way, the polarization of an electromagnetic wave is determined by a quantum mechanical property of photons called their spin. A photon can either spin in a right-hand sense or a left-hand sense about its direction of propagation. Circularly polarized electromagnetic waves are composed of photons with only one type of spin, either right- or left-hand, whereas linearly polarized waves consist of photons that are in a superposition of right and left circularly polarized states with equal amplitude, and their phases are synchronized to give oscillation in a plane.

The polarization is one of the degrees of freedom on which one can code information. Even though polarization of photons is controllable and resistant against atmospheric turbulences, the polarization states restrict the complexity of entangled states for many quantum communication tasks because they reside in a two-dimensional state-space.

This limitation is overcome with the orbital-angular momentum (OAM) modes of photons because it adds an additional dimension, obtaining a 3-D corkscrew motion that provides an unbounded state-space. Such states can carry larger amount of information per photon, and this also allows more complex types of non-classical correlations, such as entanglement of large quantum numbers, or high-dimensional entanglement, and cryptography [1].

How is this achieved?

Any electromagnetic wave carries not only energy but also momentum, which is a characteristic property of all objects in motion. The existence of this momentum becomes evident with the phenomenon called "radiation pressure" in which a light beam transfers its momentum to an absorbing or scattering object, generating a mechanical pressure on it. Light exerts pressure on objects.

Light may also carry angular momentum, which is a property of all objects in rotational motion. A light beam can be rotating around its own axis while it propagates forward, and the existence of this angular momentum is evidenced when an optical torque is induced to a small absorbing or scattering particle that receives this transfer of angular momentum during the interaction.  

The angular momentum of light is a vector quantity that expresses the amount of dynamical rotation present in the electromagnetic field of light. A light beam can be rotating, or "spinning, twisting" around its own axis, while propagating in a straight line. Two distinct forms of rotation can be found in a light beam, one involving the polarization of the electric and magnetic fields around the propagation direction -named light spin angular momentum (SAM)- and the other concerns its wavefront, in particular the helical shaped wavefront, and it is named light orbital angular momentum (OAM) [2].  


By Oleg Alexandrov - self-made with MATLAB, Public Domain,

As shown in the animated image above, a plane wavefront is the set of all points having the same phase, where the phase is an angle-like quantity representing the fraction of the cycle covered up in a rotation. In the image above, when a plane wavefront goes through a lens, its wavefront curves, meaning that the waves composing the beam have de-phased. 

Helical modes of the electromagnetic field are characterized by a wavefront that is shaped as a helix, with an optical vortex (the point of zero intensity of the beam) in the center, at the beam axis (see figure below).

The helical modes are characterized by an integer number m, positive or negative. If m = 0 the mode is not helical and the wavefronts are multiple disconnected surfaces, for example, a sequence of parallel planes (from which the name "plane wave"). If m = ± 1 m = +1 or -1, the handedness determined by the sign of m m, the wavefront is shaped as a single helical surface, with a step length equal to the wavelengthλ . Light beams that are in a helical mode carry OAM. Image by E-karimi - Own work, CC BY-SA 3.0.

In principle, photons with a twisted phase front can carry a discrete, unbounded amount of orbital angular momentum (OAM). The large state space allows for complex types of entanglement that could resist decoherence in challenging environments.

Fundamental properties of quantum physics in larger domains than the ones available inside a laboratory can be achieved by long-distance quantum entanglement with photons, opening the possibility for quantum communication between widely separated locations that could act as nodes for global quantum network. However, these long distances are expected to be difficult to obtain due to the negative influence of atmospheric turbulence on such modes.

A work from 2015 carried in Vienna and co-authored by Nobel laureate Anton Zeilinger, presents the results of an experiment in which authors show that entanglement distribution with spatial modes encoded in OAM is indeed possible over a turbulent intra-city link of 3 kilometers [3].

Their results suggests that twisted light plays a fundamental role in quantum communication systems, allowing high-speed data transmission because light can come with different amounts of twist, where each twist serves as a different channel of communication. The authors identified 11 channels available in their experiment and suggest that with the appropriate available technology there could be much more channels [4]. This possess a second limitation, how to create a secure key between parties to prevent outsiders from stealing information.

This is what the recent work by physicist Xiangdong Zhang of the Beijing Institute of Technology and his team have successfully achieved. Instead of transmitting information on multiple twisted light channels, using the same approach to record data in holograms, the photon pairs with different amounts of twist create distinct sets of data in a single hologram. As explained here, the more orbital angular momentum states involved, each with different amounts of twist, the more data researchers can pack into a hologram.

Our results show that introducing quantum entangled state into OAM holography makes the OAM holography possess infinite information channels and the transmission of information be absolute security in principle. Furthermore, decryption in the presence of strong noise is achieved.” Preprint paper [4].

This does not only packs more data into holograms, but it also increases the diversity of twists used to record the data, boosting security more than exponentially since a person needs to know or guess how the light that recorded it was twisted, in order to read the information carried by it.

As explained in the science news article, for a hologram relying on two types of twist, you would have to pick the right combination of the twists from about 80 possibilities to decode the data. Considering the combinations of seven distinct twists, this leads to millions of possibilities, which should be enough to ensure a quantum holographic encryption system.


Unified Science in Perspective-

As it is already known, a light beam can be rotating or twisting around its own axis while it propagates forward, and the existence of this angular momentum is made evident by transferring it to small absorbing or scattering particle, which is thus subject to an optical torque. But this effect is not limited to light-matter interaction, since the Casimir torque has also been discovered. This is, the OAM of the vacuum fluctuations have been proven to exist, and proven to induce torque in a material system.

What is all this implying about the quantum vacuum?

“There is only one thing … there is a field that’s spinning” - Nassim Haramein

The total angular momentum of the electromagnetic field and the other force fields, and of matter is always conserved in time. Where is the conservation of angular momentum originating from? This answer addressing the conservation of angular momentum is a critical aspect of the generalized holographic theory developed by Nassim Haramein, through which a unified field theory emerges as it is explained in his coming paper Scale invariant unification of forces, fields and particles in a Quantum Vacuum plasma [5] and the preprint The Origin of Mass and the Nature of Gravity.

As it was mentioned earlier, the more orbital angular momentum states involved, each with different amounts of twist, the more data researchers can pack into a hologram. This does not only pack more data into holograms, but it also increases the diversity of twists used to record the data, boosting security because the person needs to know how the light that recorded it was twisted in order to read the information contained within.

It is not a casual event that by means of the generalized holographic model, which explains the packing of information in any spherical system in terms of the Planck Spherical Units -PSU- being the quanta of angular momentum of the quantum vacuum- the unification of scales is being achieved, additionally proving that we live in a holographic universe where information is encoded holographically in the surface or boundary condition of rotating black holes, such as protons [6,7]. The spin and angular momentum of the quantum vacuum plasma is therefore the source of entangled and maximally protected information transfer across scales, responsible for the hologram that we call reality.



[1] Ling-Jun Kong, Yifan Sun, Furong Zhang, Jingfeng Zhang, and Xiangdong Zhang High-Dimensional Entanglement-Enabled Holography Phys. Rev. Lett. 130, 053602 (2023)


[3] Mario Krenn1,2,*, Johannes Handsteiner1,2, Matthias Fink1,2, Robert Fickler1,2,3, Anton Zeilinger, Twisted photon entanglement through turbulent air across Vienna

[4] Ling-Jun Kong, Furong Zhang, Jingfeng Zhang, Yifan Sun, and Xiangdong Zhang High-dimensional entanglement-enabled holography for quantum encryption

[5] O.Alirol and N. Haramein Scale invariant unification of forces, fields and particles in a Quantum Vacuum plasma, 

[6] Haramein, N. (2012). Quantum Gravity and the Holographic Mass, Physical Review & Research International, ISSN: 2231-1815, Page 270-292 

[7] Haramein, N. (2010). The schwarzschild proton, AIP Conference Proceedings, CP 1303, ISBN 978-0-7354-0858-6, pp. 95-100.