# 3D picture language for mathematics

There’s a new, 3D picture language for mathematics called ‘quon’ according to a March 3, 2017 news item on phys.org,

Galileo called mathematics the “language with which God wrote the universe.” He described a picture-language, and now that language has a new dimension.

The Harvard trio of Arthur Jaffe, the Landon T. Clay Professor of Mathematics and Theoretical Science, postdoctoral fellow Zhengwei Liu, and researcher Alex Wozniakowski has developed a 3-D picture-language for mathematics with potential as a tool across a range of topics, from pure math to physics.

Though not the first pictorial language of mathematics, the new one, called quon, holds promise for being able to transmit not only complex concepts, but also vast amounts of detail in relatively simple images. …

A March 2, 2017 Harvard University news release by Peter Reuell, which originated the news item, provides more context for the research,

“It’s a big deal,” said Jacob Biamonte of the Quantum Complexity Science Initiative after reading the research. “The paper will set a new foundation for a vast topic.”

“This paper is the result of work we’ve been doing for the past year and a half, and we regard this as the start of something new and exciting,” Jaffe said. “It seems to be the tip of an iceberg. We invented our language to solve a problem in quantum information, but we have already found that this language led us to the discovery of new mathematical results in other areas of mathematics. We expect that it will also have interesting applications in physics.”

When it comes to the “language” of mathematics, humans start with the basics — by learning their numbers. As we get older, however, things become more complex.

“We learn to use algebra, and we use letters to represent variables or other values that might be altered,” Liu said. “Now, when we look at research work, we see fewer numbers and more letters and formulas. One of our aims is to replace ‘symbol proof’ by ‘picture proof.’”

The new language relies on images to convey the same information that is found in traditional algebraic equations — and in some cases, even more.

“An image can contain information that is very hard to describe algebraically,” Liu said. “It is very easy to transmit meaning through an image, and easy for people to understand what they see in an image, so we visualize these concepts and instead of words or letters can communicate via pictures.”

“So this pictorial language for mathematics can give you insights and a way of thinking that you don’t see in the usual, algebraic way of approaching mathematics,” Jaffe said. “For centuries there has been a great deal of interaction between mathematics and physics because people were thinking about the same things, but from different points of view. When we put the two subjects together, we found many new insights, and this new language can take that into another dimension.”

In their most recent work, the researchers moved their language into a more literal realm, creating 3-D images that, when manipulated, can trigger mathematical insights.

“Where before we had been working in two dimensions, we now see that it’s valuable to have a language that’s Lego-like, and in three dimensions,” Jaffe said. “By pushing these pictures around, or working with them like an object you can deform, the images can have different mathematical meanings, and in that way we can create equations.”

Among their pictorial feats, Jaffe said, are the complex equations used to describe quantum teleportation. The researchers have pictures for the Pauli matrices, which are fundamental components of quantum information protocols. This shows that the standard protocols are topological, and also leads to discovery of new protocols.

“It turns out one picture is worth 1,000 symbols,” Jaffe said.

“We could describe this algebraically, and it might require an entire page of equations,” Liu added. “But we can do that in one picture, so it can capture a lot of information.”

Having found a fit with quantum information, the researchers are now exploring how their language might also be useful in a number of other subjects in mathematics and physics.

“We don’t want to make claims at this point,” Jaffe said, “but we believe and are thinking about quite a few other areas where this picture-language could be important.”

Sadly, there are no artistic images illustrating quon but this is from the paper,

An n-quon is represented by n hemispheres. We call the flat disc on the boundary of each hemisphere a boundary disc. Each hemisphere contains a neutral diagram with four boundary points on its boundary disk. The dotted box designates the internal structure that specifies the quon vector. For example, the 3-quon is represented as

Courtesy: PNAS and Harvard University

I gather the term ‘quon’ is meant to suggest quantum particles.

Here’s a link and a citation for the paper,

Quon 3D language for quantum information by Zhengwei Liu, Alex Wozniakowski, and Arthur M. Jaffe. Proceedins of the National Academy of Sciences Published online before print February 6, 2017, doi: 10.1073/pnas.1621345114 PNAS March 7, 2017 vol. 114 no. 10

This paper appears to be open access.

# 2016 thoughts and 2017 hopes from FrogHeart

This is the 4900th post on this blog and as FrogHeart moves forward to 5000, I’m thinking there will be some changes although I’m not sure what they’ll be. In the meantime, here are some random thoughts on the year that was in Canadian science and on the FrogHeart blog.

Changeover to Liberal government: year one

Hopes were high after the Trudeau government was elected. Certainly, there seems to have been a loosening where science communication policies have been concerned although it may not have been quite the open and transparent process people dreamed of. On the plus side, it’s been easier to participate in public consultations but there has been no move (perceptible to me) towards open government science or better access to government-funded science papers.

Open Science in Québec

As far as I know, la crème de la crème of open science (internationally) is the Montreal Neurological Institute (Montreal Neuro; affiliated with McGill University. They bookended the year with two announcements. In January 2016, Montreal Neuro announced it was going to be an “Open Science institution (my Jan. 22, 2016 posting),

The Montreal Neurological Institute (MNI) in Québec, Canada, known informally and widely as Montreal Neuro, has ‘opened’ its science research to the world. David Bruggeman tells the story in a Jan. 21, 2016 posting on his Pasco Phronesis blog (Note: Links have been removed),

The Montreal Neurological Institute (MNI) at McGill University announced that it will be the first academic research institute to become what it calls ‘Open Science.’  As Science is reporting, the MNI will make available all research results and research data at the time of publication.  Additionally it will not seek patents on any of the discoveries made on research at the Institute.

Will this catch on?  I have no idea if this particular combination of open access research data and results with no patents will spread to other university research institutes.  But I do believe that those elements will continue to spread.  More universities and federal agencies are pursuing open access options for research they support.  Elon Musk has opted to not pursue patent litigation for any of Tesla Motors’ patents, and has not pursued patents for SpaceX technology (though it has pursued litigation over patents in rocket technology). …

It’s one heck of a Christmas present. Canadian businessmen Larry Tannenbaum and his wife Judy have given the Montreal Neurological Institute (Montreal Neuro), which is affiliated with McGill University, a $20M donation. From a Dec. 16, 2016 McGill University news release, The Prime Minister of Canada, Justin Trudeau, was present today at the Montreal Neurological Institute and Hospital (MNI) for the announcement of an important donation of$20 million by the Larry and Judy Tanenbaum family. This transformative gift will help to establish the Tanenbaum Open Science Institute, a bold initiative that will facilitate the sharing of neuroscience findings worldwide to accelerate the discovery of leading edge therapeutics to treat patients suffering from neurological diseases.

‟Today, we take an important step forward in opening up new horizons in neuroscience research and discovery,” said Mr. Larry Tanenbaum. ‟Our digital world provides for unprecedented opportunities to leverage advances in technology to the benefit of science.  That is what we are celebrating here today: the transformation of research, the removal of barriers, the breaking of silos and, most of all, the courage of researchers to put patients and progress ahead of all other considerations.”

Neuroscience has reached a new frontier, and advances in technology now allow scientists to better understand the brain and all its complexities in ways that were previously deemed impossible. The sharing of research findings amongst scientists is critical, not only due to the sheer scale of data involved, but also because diseases of the brain and the nervous system are amongst the most compelling unmet medical needs of our time.

Neurological diseases, mental illnesses, addictions, and brain and spinal cord injuries directly impact 1 in 3 Canadians, representing approximately 11 million people across the country.

“As internationally-recognized leaders in the field of brain research, we are uniquely placed to deliver on this ambitious initiative and reinforce our reputation as an institution that drives innovation, discovery and advanced patient care,” said Dr. Guy Rouleau, Director of the Montreal Neurological Institute and Hospital and Chair of McGill University’s Department of Neurology and Neurosurgery. “Part of the Tanenbaum family’s donation will be used to incentivize other Canadian researchers and institutions to adopt an Open Science model, thus strengthening the network of like-minded institutes working in this field.”

Getting back to the federal government, we’re still waiting for a Chief Science Advisor. Should you be interested in the job, apply here. The job search was launched in early Dec. 2016 (see my Dec. 7, 2016 posting for details) a little over a year after the Liberal government was elected. I’m not sure why the process is taking so long. It’s not like the Canadian government is inventing a position or trailblazing in this regard. Many, many countries and jurisdictions have chief science advisors. Heck the European Union managed to find their first chief science advisor in considerably less time than we’ve spent on the project. My guess, it just wasn’t a priority.

Prime Minister Trudeau, quantum, nano, and Canada’s 150th birthday

In April 2016, Prime Minister Justin Trudeau stunned many when he was able to answer, in an articulate and informed manner, a question about quantum physics during a press conference at the Perimeter Institute in Waterloo, Ontario (my April 18, 2016 post discussing that incident and the so called ‘quantum valley’ in Ontario).

In Sept. 2016, the University of Waterloo publicized the world’s smallest Canadian flag to celebrate the country’s upcoming 150th birthday and to announce its presence in QUANTUM: The Exhibition (a show which will tour across Canada). Here’s more from my Sept. 20, 2016 posting,

The record-setting flag was unveiled at IQC’s [Institute of Quantum Computing at the University of Waterloo] open house on September 17 [2016], which attracted nearly 1,000 visitors. It will also be on display in QUANTUM: The Exhibition, a Canada 150 Fund Signature Initiative, and part of Innovation150, a consortium of five leading Canadian science-outreach organizations. QUANTUM: The Exhibition is a 4,000-square-foot, interactive, travelling exhibit IQC developed highlighting Canada’s leadership in quantum information science and technology.

“I’m delighted that IQC is celebrating Canadian innovation through QUANTUM: The Exhibition and Innovation150,” said Raymond Laflamme, executive director of IQC. “It’s an opportunity to share the transformative technologies resulting from Canadian research and bring quantum computing to fellow Canadians from coast to coast to coast.”

The first of its kind, the exhibition will open at THEMUSEUM in downtown Kitchener on October 14 [2016], and then travel to science centres across the country throughout 2017.

There are currently four other venues for the show once finishes its run in Waterloo. From QUANTUM’S Join the Celebration webpage,

### 2017

• Science World at TELUS World of Science, Vancouver
• TELUS Spark, Calgary
• Discovery Centre, Halifax
• Canada Science and Technology Museum, Ottawa

I gather they’re still looking for other venues to host the exhibition. If interested, there’s this: Contact us.

Other than the flag which is both nanoscale and microscale, they haven’t revealed what else will be included in their 4000 square foot exhibit but it will be “bilingual, accessible, and interactive.” Also, there will be stories.

Hmm. The exhibition is opening in roughly three weeks and they have no details. Strategy or disorganization? Only time will tell.

Calgary and quantum teleportation

This is one of my favourite stories of the year. Scientists at the University of Calgary teleported photons six kilometers from the university to city hall breaking the teleportation record. What I found particularly interesting was the support for science from Calgary City Hall. Here’s more from my Sept. 21, 2016 post,

Through a collaboration between the University of Calgary, The City of Calgary and researchers in the United States, a group of physicists led by Wolfgang Tittel, professor in the Department of Physics and Astronomy at the University of Calgary have successfully demonstrated teleportation of a photon (an elementary particle of light) over a straight-line distance of six kilometres using The City of Calgary’s fibre optic cable infrastructure. The project began with an Urban Alliance seed grant in 2014.

This accomplishment, which set a new record for distance of transferring a quantum state by teleportation, has landed the researchers a spot in the prestigious Nature Photonics scientific journal. The finding was published back-to-back with a similar demonstration by a group of Chinese researchers.

The research could not be possible without access to the proper technology. One of the critical pieces of infrastructure that support quantum networking is accessible dark fibre. Dark fibre, so named because of its composition — a single optical cable with no electronics or network equipment on the alignment — doesn’t interfere with quantum technology.

The City of Calgary is building and provisioning dark fibre to enable next-generation municipal services today and for the future.

“By opening The City’s dark fibre infrastructure to the private and public sector, non-profit companies, and academia, we help enable the development of projects like quantum encryption and create opportunities for further research, innovation and economic growth in Calgary,” said Tyler Andruschak, project manager with Innovation and Collaboration at The City of Calgary.

As for the science of it (also from my post),

A Sept. 20, 2016 article by Robson Fletcher for CBC (Canadian Broadcasting News) online provides a bit more insight from the lead researcher (Note: A link has been removed),

“What is remarkable about this is that this information transfer happens in what we call a disembodied manner,” said physics professor Wolfgang Tittel, whose team’s work was published this week in the journal Nature Photonics.

“Our transfer happens without any need for an object to move between these two particles.”

A Sept. 20, 2016 University of Calgary news release by Drew Scherban, which originated the news item, provides more insight into the research,

“Such a network will enable secure communication without having to worry about eavesdropping, and allow distant quantum computers to connect,” says Tittel.

Experiment draws on ‘spooky action at a distance’

The experiment is based on the entanglement property of quantum mechanics, also known as “spooky action at a distance” — a property so mysterious that not even Einstein could come to terms with it.

“Being entangled means that the two photons that form an entangled pair have properties that are linked regardless of how far the two are separated,” explains Tittel. “When one of the photons was sent over to City Hall, it remained entangled with the photon that stayed at the University of Calgary.”

Next, the photon whose state was teleported to the university was generated in a third location in Calgary and then also travelled to City Hall where it met the photon that was part of the entangled pair.

“What happened is the instantaneous and disembodied transfer of the photon’s quantum state onto the remaining photon of the entangled pair, which is the one that remained six kilometres away at the university,” says Tittel.

Council of Canadian Academies and The State of Science and Technology and Industrial Research and Development in Canada

Preliminary data was released by the CCA’s expert panel in mid-December 2016. I reviewed that material briefly in my Dec. 15, 2016 post but am eagerly awaiting the full report due late 2017 when, hopefully, I’ll have the time to critique the material, and which I hope will have more surprises and offer greater insights than the preliminary report did.

Colleagues

Thank you to my online colleagues. While we don’t interact much it’s impossible to estimate how encouraging it is to know that these people continually participate and help create the nano and/or science blogosphere.

David Bruggeman at his Pasco Phronesis blog keeps me up-to-date on science policy both in the US, Canada, and internationally, as well as, keeping me abreast of the performing arts/science scene. Also, kudos to David for raising my (and his audience’s) awareness of just how much science is discussed on late night US television. Also, I don’t know how he does it but he keeps scooping me on Canadian science policy matters. Thankfully, I’m not bitter and hope he continues to scoop me which will mean that I will get the information from somewhere since it won’t be from the Canadian government.

Tim Harper of Cientifica Research keeps me on my toes as he keeps shifting his focus. Most lately, it’s been on smart textiles and wearables. You can download his latest White Paper titled, Fashion, Smart Textiles, Wearables and Disappearables, from his website. Tim consults on nanotechnology and other emerging technologies at the international level.

Dexter Johnson of the Nanoclast blog on the IEEE (Institute of Electrical and Electronics Engineers) website consistently provides informed insight into how a particular piece of research fits into the nano scene and often provides historical details that you’re not likely to get from anyone else.

Dr. Andrew Maynard is currently the founding Director of the Risk Innovation Lab at the University of Arizona. I know him through his 2020 Science blog where he posts text and videos on many topics including emerging technologies, nanotechnologies, risk, science communication, and much more. Do check out 2020 Science as it is a treasure trove.

2017 hopes and dreams

I hope Canada’s Chief Science Advisor brings some fresh thinking to science in government and that the Council of Canadian Academies’ upcoming assessment on The State of Science and Technology and Industrial Research and Development in Canada is visionary. Also, let’s send up some collective prayers for the Canada Science and Technology Museum which has been closed since 2014 (?) due to black mold (?). It would be lovely to see it open in time for Canada’s 150th anniversary.

I’d like to see the nanotechnology promise come closer to a reality, which benefits as many people as possible.

As for me and FrogHeart, I’m not sure about the future. I do know there’s one more Steep project (I’m working with Raewyn Turner on a multiple project endeavour known as Steep; this project will involve sound and gold nanoparticles).

Should anything sparkling occur to me, I will add it at a future date.

In the meantime, Happy New Year and thank you from the bottom of my heart for reading this blog!

# Teleportation of a classic object (Star Trek’s teleportation)

A March 4, 2016 Friedrich-Schiller-Universitaet Jena press release (also on EurekAlert) describes the work in terms of Star Trek,

“Beam me up, Scotty” – even if Captain Kirk supposedly never said this exact phrase, it remains a popular catch-phrase to this day. Whenever the chief commander of the television series starship USS Enterprise (NCC-1701) wanted to go back to his control centre, this command was enough to take him back to the control centre instantly – travelling through the infinity of outer space without any loss of time.

But is all of this science fiction that was thought up in the 1960s? Not quite: Physicists are actually capable of beaming–or “teleporting” as it is called in technical language – if not actual solid particles at least their properties.

“Many of the ideas from Star Trek that back then appeared to be revolutionary have become reality,” explains Prof. Dr Alexander Szameit from the University of Jena (Germany). “Doors that open automatically, video telephony or flip phones–all things we have first seen on the starship USS Enterprise,” exemplifies the Juniorprofessor of Diamond-/Carbon-Based Optical Systems. So why not also teleporting? “Elementary particles such as electrons and light particles exist per se in a spatially delocalized state,” says Szameit. For these particles, it is with a certain probability thus possible to be in different places at the same time. “Within such a system spread across multiple locations, it is possible to transmit information from one location to another without any loss of time.” This process is called quantum teleportation and has been known for several years.

The team of scientists lead by science fiction fan Szameit has now for the first demonstrated in an experiment that the concept of teleportation does not only persist in the world of quantum particles, but also in our classical world. …

They used a special form of laser beams in the experiment. “As can be done with the physical states of elementary particles, the properties of light beams can also be entangled,” explains Dr Marco Ornigotti, a member of Prof. Szameit’s team. For physicists, “entanglement” means a sort of codification. “You link the information you would like to transmit to a particular property of the light,” clarifies Ornigotti who led the experiments for the study that was now presented.

In their particular case, the physicists have encoded some information in a particular polarisation direction of the laser light and have transmitted this information to the shape of the laser beam using teleportation. “With this form of teleportation, we can, however, not bridge any given distance,” admits Szameit. “On the contrary, classic teleportation only works locally.” But just like it did at the starship USS Enterprise or in quantum teleportation, the information is transmitted fully and instantly, without any loss of time. And this makes this kind of information transmission a highly interesting option in telecommunication for instance, underlines Szameit.

Here’s a link to and a citation for the paper,

Demonstration of local teleportation using classical entanglement by Diego Guzman-Silva, Robert Brüning, Felix Zimmermann, Christian Vetter, Markus Gräfe, Matthias Heinrich, Stefan Nolte, Michael Duparré, Andrea Aiello, Marco Ornigotti and Alexander Szameit. Laser & Photonics Reviews DOI: 10.1002/lpor.201500252 Article first published online: 11 JAN 2016

© 2016 by WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

This paper is behind a paywall.

# Quantum teleportation

It’s been two years (my Aug. 16, 2013 posting features a German-Japanese collaboration) since the last quantum teleportation posting here. First, a little visual stimulation,

Captain James T Kirk (credit: http://www.comicvine.com/james-t-kirk/4005-20078/)

Captain Kirk, also known as William Shatner, is from Montréal, Canada and that’s not the only Canadian connection to this story which is really about some research at York University (UK). From an Oct. 1, 2015 news item on Nanotechnology Now,

Mention the word ‘teleportation’ and for many people it conjures up “Beam me up, Scottie” images of Captain James T Kirk.

But in the last two decades quantum teleportation – transferring the quantum structure of an object from one place to another without physical transmission — has moved from the realms of Star Trek fantasy to tangible reality.

A Sept. 30, 2015 York University (UK) press release, which originated the news item, describes the quantum teleportation research problem and solution,

Quantum teleportation is an important building block for quantum computing, quantum communication and quantum network and, eventually, a quantum Internet. While theoretical proposals for a quantum Internet already exist, the problem for scientists is that there is still debate over which of various technologies provides the most efficient and reliable teleportation system. This is the dilemma which an international team of researchers, led by Dr Stefano Pirandola of the Department of Computer Science at the University of York, set out to resolve.

In a paper published in Nature Photonics, the team, which included scientists from the Freie Universität Berlin and the Universities of Tokyo and Toronto [emphasis mine], reviewed the theoretical ideas around quantum teleportation focusing on the main experimental approaches and their attendant advantages and disadvantages.

None of the technologies alone provide a perfect solution, so the scientists concluded that a hybridisation of the various protocols and underlying structures would offer the most fruitful approach.

For instance, systems using photonic qubits work over distances up to 143 kilometres, but they are probabilistic in that only 50 per cent of the information can be transported. To resolve this, such photon systems may be used in conjunction with continuous variable systems, which are 100 per cent effective but currently limited to short distances.

Most importantly, teleportation-based optical communication needs an interface with suitable matter-based quantum memories where quantum information can be stored and further processed.

Dr Pirandola, who is also a member of the York Centre for Quantum Technologies, said: “We don’t have an ideal or universal technology for quantum teleportation. The field has developed a lot but we seem to need to rely on a hybrid approach to get the best from each available technology.

“The use of quantum teleportation as a building block for a quantum network depends on its integration with quantum memories. The development of good quantum memories would allow us to build quantum repeaters, therefore extending the range of teleportation. They would also give us the ability to store and process the transmitted quantum information at local quantum computers.

“This could ultimately form the backbone of a quantum Internet. The revised hybrid architecture will likely rely on teleportation-based long-distance quantum optical communication, interfaced with solid state devices for quantum information processing.”

Here’s a link to and a citation for the paper,

Advances in quantum teleportation by S. Pirandola, J. Eisert, C. Weedbrook, A. Furusawa, & S. L. Braunstein. Nature Photonics 9, 641–652 (2015) doi:10.1038/nphoton.2015.154 Published online 29 September 2015

This paper is behind a paywall.

# Quantum teleportation from a Japan-Germany collaboration

An Aug. 15, 2013 Johannes Gutenberg University Mainz press release (also on EurekAlert) has somewhat gobsmacked me with its talk of teleportation,

By means of the quantum-mechanical entanglement of spatially separated light fields, researchers in Tokyo and Mainz have managed to teleport photonic qubits with extreme reliability. This means that a decisive breakthrough has been achieved some 15 years after the first experiments in the field of optical teleportation. The success of the experiment conducted in Tokyo is attributable to the use of a hybrid technique in which two conceptually different and previously incompatible approaches were combined. “Discrete digital optical quantum information can now be transmitted continuously – at the touch of a button, if you will,” explained Professor Peter van Loock of Johannes Gutenberg University Mainz (JGU). As a theoretical physicist, van Loock advised the experimental physicists in the research team headed by Professor Akira Furusawa of the University of Tokyo on how they could most efficiently perform the teleportation experiment to ultimately verify the success of quantum teleportation.

The press release goes on to describe quantum teleportation,

Quantum teleportation involves the transfer of arbitrary quantum states from a sender, dubbed Alice, to a spatially distant receiver, named Bob. This requires that Alice and Bob initially share an entangled quantum state across the space in question, e.g., in the form of entangled photons. Quantum teleportation is of fundamental importance to the processing of quantum information (quantum computing) and quantum communication. Photons are especially valued as ideal information carriers for quantum communication since they can be used to transmit signals at the speed of light. A photon can represent a quantum bit or qubit analogous to a binary digit (bit) in standard classical information processing. Such photons are known as ‘flying quantum bits.

Before explaining the new technique, there’s an overview of previous efforts,

The first attempts to teleport single photons or light particles were made by the Austrian physicist Anton Zeilinger. Various other related experiments have been performed in the meantime. However, teleportation of photonic quantum bits using conventional methods proved to have its limitations because of experimental deficiencies and difficulties with fundamental principles.

What makes the experiment in Tokyo so different is the use of a hybrid technique. With its help, a completely deterministic and highly reliable quantum teleportation of photonic qubits has been achieved. The accuracy of the transfer was 79 to 82 percent for four different qubits. In addition, the qubits were teleported much more efficiently than in previous experiments, even at a low degree of entanglement.

The concept of entanglement was first formulated by Erwin Schrödinger and involves a situation in which two quantum systems, such as two light particles for example, are in a joint state, so that their behavior is mutually dependent to a greater extent than is normally (classically) possible. In the Tokyo experiment, continuous entanglement was achieved by means of entangling many photons with many other photons. This meant that the complete amplitudes and phases of two light fields were quantum correlated. Previous experiments only had a single photon entangled with another single photon – a less efficient solution. “The entanglement of photons functioned very well in the Tokyo experiment – practically at the press of a button, as soon as the laser was switched on,” said van Loock, Professor for Theory of Quantum Optics and Quantum Information at Mainz University. This continuous entanglement was accomplished with the aid of so-called ‘squeezed light’, which takes the form of an ellipse in the phase space of the light field. Once entanglement has been achieved, a third light field can be attached to the transmitter. From there, in principle, any state and any number of states can be transmitted to the receiver. “In our experiment, there were precisely four sufficiently representative test states that were transferred from Alice to Bob using entanglement. Thanks to continuous entanglement, it was possible to transmit the photonic qubits in a deterministic fashion to Bob, in other words, in each run,” added van Loock.

Earlier attempts to achieve optical teleportation were performed differently and, before now, the concepts used have proved to be incompatible. Although in theory it had already been assumed that the two different strategies, from the discrete and the continuous world, needed to be combined, it represents a technological breakthrough that this has actually now been experimentally demonstrated with the help of the hybrid technique. “The two separate worlds, the discrete and the continuous, are starting to converge,” concluded van Loock.

The researchers have provided an image illustrating quantum teleportation,

Deterministic quantum teleportation of a photonic quantum bit. Each qubit that flies from the left into the teleporter leaves the teleporter on the right with a loss of quality of only around 20 percent, a value not achievable without entanglement. Courtesy University of Tokyo

Here’s a citation for and a link to the published paper,

Deterministic quantum teleportation of photonic quantum bits by a hybrid technique by Shuntaro Takeda, Takahiro Mizuta, Maria Fuwa, Peter van Loock & Akira Furusawa. Nature 500, 315–318 (15 August 2013) doi:10.1038/nature12366 Published online 14 August 2013