The extraordinary promise of quantum technology—depend on quantum “entanglement,” in which the physical states of two or more objects such as atoms, photons or ions become so inextricably connected that the state of one particle can instantly influence the state of the other—no matter how far apart they are. Today, entanglement is actively being explored as a resource for future technologies including quantum computers, quantum communication networks and high-precision quantum sensors.

In previous studies, photons have typically been entangled by one dimension of their quantum properties — usually the direction of their polarization. Hyperentanglement is a state of (two photons) being simultaneously entangled in multiple degrees of freedom such as polarization, energy-time, spatial mode, orbit-angular-momentum, time-bin and frequency DOFs of photons.

With each dimension of entanglement, the amount of information carried on a photon pair is doubled, so a photon pair entangled by five dimensions can carry 32 times as much data as a pair entangled by only one. Another advantage of using such a system is that it is relatively easy to perform quantum logic between qubits residing in different degrees of freedom of the same photon, as opposed to qubits residing in different photons.

Increasing the dimensionality of quantum entanglement is a key enabler for high-capacity quantum communications. Quantum cryptography (QKD) is an emerging technology in which two parties may simultaneously generate shared, secret cryptographic key material using the transmission of quantum states of light. QKD uses quantum superpositions and quantum entanglement and transmitting information in quantum states, to implement the communication system that detects eavesdropping. Current QKD systems are their slow key generation rate and limited range. The “unconditionally secure” system needs one bit of key for each bit of data, but current QKD systems generate key material far too slowly for this form of encryption.

Potential applications for the research include secure communication and information processing, in particular for high-capacity data transfer with minimal error. This could be useful for medical servers, government data communications, financial markets and military communication channels, as well as quantum cloud communications and distributed quantum computing.

### In 2015, UCLA verified that new method of quantum entanglement, Hyperentanglement vastly increases how much information can be carried in a photon

Quantum entanglement allow users to send data through a network and know immediately whether that data had made it to its destination without being intercepted or altered. With hyper entanglement, users could send much denser packets of information using the same networks.

Research team led by engineers from UCLA has verified that it is possible to break up and entangle photon pairs into many dimensions using properties such as the photons’ energy and spin. In secure data transfer, photons sent over fiber optic networks can be encrypted through entanglement. To achieve this, the researchers transmitted hyperentangled photons in the form of a biphoton frequency comb (essentially a series of individual, equidistantly-arranged frequencies) that divided up the entangled photons into smaller parts.

An extension of the technique of wavelength-division multiplexing (the process used to simultaneously transmit things such as multiple video signals over a single optical fiber), the biphoton frequency comb demonstrates the useful applications of such methods not just at macro levels, but quantum ones as well. “We show that an optical frequency comb can be generated at single photon level,” says Zhenda Xie, associate professor and research scientist at UCLA. “Essentially, we’re leveraging wavelength division multiplexing concepts at the quantum level.”

“Our goal is to advance quantum hyperentanglement for high-speed, unbreakable, secure communications,” says Chee Wei Wong, Sc.D., associate professor of electrical engineering. “This is an enhancement package to dramatically speed up the current Quantum Key Distribution (QKD) rate, so our breakthrough leverages on the current QKD technologies, some of which are already implemented and released.”

Wong explains that this technology is relevant for transmitting medical databases, finance trading and banking information, government database communications and military communications in the field and war theatre.

“The next step for us,” says Wong, “is to demonstrate even more quantum bits encoded in the hyperentanglement approach. Currently, each photon carries about five quantum bits, at about 2^5 = 32 (2 to the 5th power), which is 32 times higher than the current unbreakable data rates. As the next step, we would also like to see information encoding on our physical system.” The work was funded by the Defense Advanced Research Projects Agency.

In 2020 it was reported that Scientists have just packed 18 qubits — the most basic units of quantum computing — into just six weirdly connected photons. That’s an unprecedented three qubits per photon, and a record for the number of qubits linked to one another via quantum entanglement.

The achievement, according to Sydney Schreppler, a quantum physicist at the University of California, Berkeley who was not involved in the research, was likely only possible because the team at the University of Science and Technology of China (USTC) managed to pack so many qubits into so few particles. “If the goal is to make 18, the way groups … would have done that in the past is to make 18 entangled particles with one [qubit] each,” she said. “It’s going to be a slow process.”

It takes “many seconds” to entangle just the six particles used in the experiment, she said — already an eternity in computer time, where a new entanglement process must begin for each calculation. And each additional particle added to the entanglement takes longer to join the party than the last, to the point that it would be completely unreasonable to build an 18-qubit entanglement, one qubit at a time. (There are plenty of quantum experiments involving more than 18 qubits, but in those experiments, the qubits aren’t all entangled. Instead, the systems entangle just a few neighboring qubits for each calculation.)

To pack each of the six entangled particles (photons, in this case) with three qubits, the researchers took advantage of the photons’ “multiple degrees of freedom,” they reported in a paper that was published June 28 in the journal Physical Review Letters and is also available on the server arXiv. When a qubit is encoded into a particle, it’s encoded into one of the states the particle can flip back and forth between — like its polarization, or its quantum spin. Each of those is a “degree of freedom.” A typical quantum experiment involves just one degree of freedom across all the particles involved. But particles like photons have many degrees of freedom. And by coding using more than one of those at the same time — something researchers have dabbled in before, but not to this extreme, Schreppler said — a quantum system can pack a lot more information into fewer particles. “It’s as though you took six bits in your computer, but each bit tripled in how much information it could hold,” Schreppler said, “and they can do that pretty quickly and pretty efficiently.”

The fact that the USTC researchers pulled off this experiment, she said, doesn’t mean quantum computing experiments elsewhere will start to involve many more degrees of freedom at a time. Photons are particularly useful for certain kinds of quantum operations, she said — most importantly, quantum networking, in which information is transmitted among multiple quantum computers. But other forms of qubits, like those in the superconducting circuits Schreppler works on, might not take to this kind of operation as easily. One open question from the paper, she said, is whether all of the entangled qubits interact equally, or whether there are differences between qubit interactions on the same particle or qubit interactions across different degrees of freedom. Down the road, the researchers wrote in the paper, this sort of experimental setup might allow for certain quantum calculations that, until now, had been discussed only theoretically and had never been put into action.

### In Nov 2018 University of Vienna and the Austrian Academy of Sciences entangled three photons for complex quantum teleportation

Scientists from the University of Vienna and the Austrian Academy of Sciences have broken new ground. They sought to use more complex quantum systems than two-dimensionally entangled qubits and thus can increase the information capacity with the same number of particles. The developed methods and technologies could in the future enable the teleportation of complex quantum systems. The results of their work, “Experimental Greenberger-Horne-Zeilinger entanglement beyond qubits,” is published recently in the renowned journal Nature Photonics.

“The special thing about our experiment is that for the first time, it entangles three photons beyond the conventional two-dimensional nature,” explains Manuel Erhard, first author of the study. For this purpose, the Viennese physicists used quantum systems with more than two possible states—in this particular case, the angular momentum of individual light particles. These individual photons now have a higher information capacity than qubits. However, the entanglement of these light particles turned out to be difficult on a conceptual level. The researchers overcame this challenge with a groundbreaking idea: a computer algorithm that autonomously searches for an experimental implementation.

With the help of a computer algorithm called Melvin, the researchers found an experimental setup to produce this type of entanglement. At first, this was very complex, but it worked in principle. After some simplifications, the physicists still faced major technological challenges. The team was able to solve these with state-of-the-art laser technology and a specially developed multi-port. “This multi-port is the heart of our experiment, and combines the three photons so that they are entangled in three dimensions,” explains Manuel Erhard.

The peculiar property of the three-photon entanglement in three dimensions allows for experimental investigation of new fundamental questions about the behaviour of quantum systems. In addition, the results of this work could also have a significant impact on future technologies, such as quantum teleportation. “I think the methods and technologies that we developed in this publication allow us to teleport a higher proportion of the total quantum information of a single photon, which could be important for quantum communication networks,” Anton Zeilinger says.

### Chinese Quantum entanglement breakthroughs

In 2018, Scientists at China’s Academy of Sciences’ Key Laboratory of Quantum Information deployed high-fidelity four-dimensional entanglement in quantum superdense coding (SDC). The successful use of this high-dimensional quantum entanglement overhauls the functionality of quantum information processing, rendering it safer and more efficient, according to the findings of the lab at the University of Science and Technology of China in Hefei, East China’s Anhui Province.

High-dimensional entanglement not only has better efficiency in information communication, but also better resistance against environmental disturbance, “making it even more difficult to crack,” Li Chuanfeng, laboratory executive deputy director told the Global Times. High-dimensional entanglement will make a future quantum network possible, in which information storage and transmission will be safer and more efficient, Li said. Their experiment achieved 98 percent “fidelity,” or accuracy, surpassing the limits of previous two-dimensional two-quantum bit (qubit) entanglement. To achieve the breakthrough in high-quality, high-dimensional entangled states, the Chinese team had to link up a high fidelity four-dimensional entanglement device and distinguish between five four-dimensional Bell states.

### Provably secure and high-rate quantum key distribution with time-bin qudits

**In 2015, New approach developed that used “twisted light” to increase the efficiency of quantum cryptography systems**

Researchers at the University of Rochester and their collaborators have developed a way to transfer 2.05 bits per photon by using “twisted light.” This remarkable achievement is possible because the researchers used the orbital angular momentum of the photons to encode information, rather than the more commonly used polarization of light. The new approach doubles the 1 bit per photon that is possible with current systems that rely on light polarization and could help increase the efficiency of quantum cryptography systems.

Basically, light has energy defined by its frequency and momentum defined by its wavelength. The orbital angular momentum is the wavefront of a beam of light that’s coiling around its propagation axis. The electric field spirals around like a corkscrew; hence, twisted light. The quantum number describes how sharp the spiral is, while the sign reveals the direction of the spiral.

Quantum cryptography promises more secure communications. The first step in such systems is quantum key distribution (QKD), to ensure that both the sender and receiver – usually referred to as Alice and Bob – are communicating in such a way that only they know what is being sent. They are the only ones who hold the “key” to the messages, and the systems are set up in such a way that the presence of any eavesdropper would be identified.

In the paper, published in New Journal of Physics, Mohammad Mirhosseini and his colleagues describe a proof-of-principle experiment that shows that using OAM to encode information rather than polarization opens up the possibility of high-dimensional QKD. Mirhosseini, a Ph.D. student in Robert W. Boyd’s group at the University of Rochester’s Institute of Optics, explains that they were able to encode a seven dimensional “alphabet” – that is, seven letters or symbols – using both the orbital angular momentum (OAM) of the photons and their angular position (ANG). These two properties of the photons form what physicists refer to as mutually unbiased bases, a requirement for QKD. Using mutually unbiased bases, the correct answer is revealed only if Alice encodes the information using a particular basis and Bob measures in that same basis

In QKD, once they have generated a long, shared key, Alice and Bob publicly announce the basis (or “alphabet”) they have used for each symbol in the key. They then compare what alphabet was used for sending and which one for receiving. They only keep the part of the key in which they have used the same “alphabet.” The letters they keep produce a secure key, which they can use to encrypt messages and transmit these with regular encryption without the need for quantum cryptography.

If for any reason their communication is intercepted, because of a fundamental property of quantum mechanics, there will be discrepancies between Alice and Bob’s keys. To check for this, Alice and Bob sacrifice a short part of their key. They share this publicly and identify any discrepancies. This lets them know whether their connection is secure and, if not, they will stop the communication.

The researchers showed that using their system they were able to generate and detect information at a rate of 4kHz and with 93% accuracy. A long term goal of the research is to realize secure communications at GHz transmission rates, which is desirable for telecommunication applications.

“Our experiment shows that it is possible to use “twisted light” for QKD and that it doubles the capacity compared to using polarization,” said Mirhosseini. “Unlike with polarization, where it is impossible to encode more than one bit per photon, “twisted light” could make it possible to encode several bits, and every extra bit of information encoded in a photon means fewer photons to generate and measure.”

In a previous experiment using a strong laser beam instead of single photons, Boyd’s team were able to measure up to 25 modes of OAM and ANG. This is equivalent to having 25 letters available in your “alphabet” rather than 7. This shows the potential for a system like the one described in the new paper to have the capacity to transmit and measure 4.17 bits per photon using more sophisticated equipment.

Our experiment demonstrates that, in addition to having an increased information capacity, multilevel QKDsystems based on spatial-mode encoding can be more resilient against intercept-resend eavesdropping attacks.

** **

**Three “twisted” photons in three dimensions**

Researchers at the Institute of Quantum Optics and Quantum Information (IQOQI), the University of Vienna, and the Universitat Autonoma de Barcelona have achieved a new milestone in quantum physics: they were able to entangle three particles of light in a high-dimensional quantum property related to the “twist” of their wavefront structure.

Entanglement is a counterintuitive property of quantum physics that has long puzzled scientists and philosophers alike. Entangled quanta of light seem to exert an influence on each other, irrespective of how much distance is between them. Consider for example a metaphorical quantum ice dancer, who has the uncanny ability to pirouette both clockwise and counter-clockwise simultaneously. A pair of entangled ice-dancers whirling away from each other would then have perfectly correlated directions of rotation: If the first dancer twirls clockwise then so does her partner, even if skating in ice rinks on two different continents. “The entangled photons in our experiment can be illustrated by not two, but three such ice dancers, dancing a perfectly synchronized quantum mechanical ballet,” explains Mehul Malik, the first author of the paper. “Their dance is also a bit more complex, with two of the dancers performing yet another correlated movement in addition to pirouetting. This type of asymmetric quantum entanglement has been predicted before on paper, but we are the first to actually create it in the lab.”

** **

**From fundamentals to applications: Layered quantum cryptography**

The scientists created their three-photon entangled state by using yet another quantum mechanical trick: they combined two pairs of high-dimensionally entangled photons in such a manner that it became impossible to ascertain where a particular photon came from.

Besides serving as a test bed for studying many fundamental concepts in quantum mechanics, multi-photon entangled states such as these have applications ranging from quantum computing to quantum encryption. Along these lines, the authors of this study have developed a new type of quantum cryptographic protocol using their state that allows different layers of information to be shared asymmetrically among multiple parties with unconditional security.

“The experiment opens the door for a future quantum Internet with more than two partners and it allows them to communicate more than one bit per photon,” says Anton Zeilinger. Many technical challenges remain before such a quantum communication protocol becomes a practical reality. However, given the rapid progress in quantum technologies today, it is only a matter of time before this type of entanglement finds a place in the quantum networks of the future.

This research was supported by the European Commission, the European Research Council (ERC) and the Austrian Science Fund (FWF).

**Researchers refined method for detecting quantum entanglement in 2016**

RMIT quantum computing researchers have developed and demonstrated a method capable of efficiently detecting high-dimensional entanglement. Entanglement in quantum physics is the ability of two or more particles to be related to each other in ways which are beyond what is possible in classical physics. Having information on a particle in an entangled ensemble reveals an “unnatural” amount of information on the other particles.

The researchers’ paper, “High-dimensional entanglement certification”, is published in Scientific Reports. Dr Alberto Peruzzo, a senior research fellow with RMIT University’s School of Engineering and Director of RMIT’s Quantum Photonics Laboratory, said: “The method we developed employs only two local measurements of complementary properties. This procedure can also certify whether the system is maximally entangled.”

Full-scale quantum computing relies heavily on entanglement between the individual particles used to store information, the quantum bits, or qubits. Quantum computing promises to exponentially speed up certain tasks because entanglement allows a vastly increased amount of information to be stored and processed with the same number of qubits.

Peruzzo said: “Together with this increase also comes the problem of needing to measure the device many times to Ònd out what it is truly doing – that is, before the quantum computer is up and running, we need to gather an exponentially large amount of information on how it is performing.” Zixin Huang, a PhD student working on the experiment, said: “The current form of computer encodes information in binary form. A higher dimensional state, however, is a particle that contains a message that can be 0, 1, 2 or more, so much more information can be stored and transmitted. “To date, tools for characterising high-dimensional entangled states are limited. In the future when quantum computers become available, our method can potentially serve as a tool in certifying whether the system has enough entanglement between the qubits. “It significantly cuts down on the number of measurements needed – in fact, it needs the least number of measurements per dimension. Additionally, unlike some others, this method works for systems of any dimension.”

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