Computers Math

In some versions of the game blackjack, one way to win against the house is for players at the table to work as a team to keep track of and covertly communicate amongst each other the cards they have been dealt. With that knowledge, they can then estimate the cards still in the deck, and those most likely to be dealt out next, all to help each player decide how to place their bets, and as a team, gain an advantage over the dealer.
This calculating strategy, known as card-counting, was made famous by the MIT Blackjack Team, a group of students from MIT, Harvard University, and Caltech, who for several decades starting in 1979, optimized card-counting and other techniques to successfully beat casinos at blackjack around the world — a story that later inspired the book “Bringing Down the House.”
Now researchers at MIT and Caltech have shown that the weird, quantum effects of entanglement could theoretically give blackjack players even more of an edge, albeit a small one, when playing against the house.
In a paper published this week in the journal Physical Review A, the researchers lay out a theoretical scenario in which two players, playing cooperatively against the dealer, can better coordinate their strategies using a quantumly entangled pair of systems. Such systems exist now in the laboratory, although not in forms convenient for any practical use in casinos. In their study, the authors nevertheless explore the theoretical possibilities for how a quantum system might influence outcomes in blackjack.
They found that such quantum communication would give the players a slight advantage compared to classical card-counting strategies, though in limited situations where the number of cards left in the dealer’s deck is low.
“It’s pretty small in terms of the actual magnitude of the expected quantum advantage,” says first author Joseph Lin, a former graduate student at MIT. “But if you imagine the players are extremely rich, and the deck is really low in number, so that every card counts, these small advantages can be big. The exciting result is that there’s some advantage to quantum communication, regardless of how small it is.”
Lin’s MIT co-authors on the paper are professor of physics Joseph Formaggio, associate professor of physics Aram Harrow, and Anand Natarajan of Caltech, who will start at MIT in September as assistant professor of electrical engineering and computer science.

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Quantum dealings
Entanglement is a phenomenon described by the rules of quantum mechanics, which states that two physically separate objects can be “entangled,” or correlated with each other, in such a way that the correlations between them are stronger than what would be predicted by the classical laws of physics and probability.
In 1964, physicist John Bell proved mathematically that quantum entanglement could exist, and also devised a test — known a Bell test — that scientists have since applied to many scenarios to ascertain if certain spatially remote particles or systems behave according to classical, real-world physics, or whether they may exhibit some quantum, entangled states.
“One motivation for this work was as a concrete realization of the Bell test,” says Harrow of the team’s new paper. “People wrote the rules of blackjack not thinking of entanglement. But the players are dealt cards, and there are some correlations between the cards they get. So does entanglement work here? The answer to the question was not obvious going into it.”
After casually entertaining the idea during a regular poker night with friends, Formaggio decided to explore the possibility of quantum blackjack more formally with his MIT colleagues.

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“I was grateful to them for not laughing and closing the door on me when I brought up the idea,” Formaggio recalls.
Correlated cards
In blackjack, the dealer deals herself and each player a face-up card that is public to all, and a face-down card. With this information, each player decides whether to “hit,” and be dealt another card, or “stand,” and stay with the cards they have. The goal after one round is to have a hand with a total that is closer to 21, without going over, than the dealer and the other players at the table.
In their paper, the researchers simulated a simple blackjack setup involving two players, Alice and Bob, playing cooperatively against the dealer. They programmed Alice to consistently bet low, with the main objective of helping Bob, who could hit or stand based on any information he gained from Alice.
The researchers considered how three different scenarios might help the players win over the dealer: a classical card-counting scenario without communication; a best-case scenario in which Alice simply shows Bob her face-down card, demonstrating the best that a team can do in playing against the dealer; and lastly, a quantum entanglement scenario.
In the quantum scenario, the researchers formulated a mathematical model to represent a quantum system, which can be thought of abstractedly as a box with many “buttons,” or measurement choices, that is shared between Alice and Bob.
For instance, if Alice’s face-down card is a 5, she can push a particular button on the quantum box and use its output to inform her usual choice of whether to hit or stand. Bob, in turn, looks at his face-down card when deciding which button to push on his quantum box, as well as whether to use the box at all. In the cases where Bob uses his quantum box, he can combine its output with his observation of Alice’s strategy to decide his own move. This extra information — not exactly the value of Alice’s card, but more information than a random guess — can help Bob decide whether to hit or stand.
The researchers ran all three scenarios, with many combinations of cards between each player and the dealer, and with increasing number of cards left in the dealer’s deck, to see how often Alice and Bob could win against the dealer.
After running thousands of rounds for each of the three scenarios, they found that the players had a slight advantage over the dealer in the quantum entanglement scenario, compared with the classical card-counting strategy, though only when a handful of cards were left in the dealer’s deck.
“As you increase the deck and therefore increase all the possibilities of different cards coming to you, the fact that you know a little bit more through this quantum process actually gets diluted,” Formaggio explains.
Nevertheless, Harrow notes that “it was surprising that these problems even matched, that it even made sense to consider entangled strategy in blackjack.”
Do these results mean that future blackjack teams might use quantum strategies to their advantage?
“It would require a very large investor, and my guess is, carrying a quantum computer in your backpack will probably tip the house,” Formaggio says. “We think casinos are safe right now from this particular threat.” More

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The fields of condensed matter physics and material science are intimately linked because new physics is often discovered in materials with special arrangements of atoms. Crystals, which have repeating units of atoms in space, can have special patterns which result in exotic physical properties. Particularly exciting are materials which host multiple types of exotic properties because they give scientists the opportunity to study how those properties interact with and influence each other. The combinations can give rise to unexpected phenomena and fuel years of basic and technological research.
In a new study published in Science Advances this week, an international team of scientists from the USA, Columbia, Czech Republic, England, and led by Dr. Mazhar N. Ali at the Max Planck Institute of Microstructure Physics in Germany, has shown that a new material, KV3Sb5, has a never-seen-before combination of properties that results in one of the largest anomalous Hall effects (AHEs) ever observed; 15,500 siemens per centimeter at 2 Kelvin.
Discovered in the lab of co-author Prof. Tyrel McQueen at Johns Hopkins University, KV3Sb5 combines four properties into one material: Dirac physics, metallic frustrated magnetism, 2D exfoliability (like graphene), and chemical stability.
Dirac physics, in this context, relates to the fact that the electrons in KV3Sb5 aren’t just your normal run-of-the-mill electrons; they are moving extremely fast with very low effective mass. This means that they are acting “light-like”; their velocities are becoming comparable to the speed of light and they are behaving as though they have only a small fraction of the mass which they should have. This results in the material being highly metallic and was first shown in graphene about 15 years ago.
The “frustrated magnetism” arises when the magnetic moments in a material (imagine little bar magnets which try to turn each other and line up North to South when you bring them together) are arranged in special geometries, like triangular nets. This scenario can make it hard for the bar magnets to line up in way that they all cancel each other out and are stable. Materials exhibiting this property are rare, especially metallic ones. Most frustrated magnet materials are electrical insulators, meaning that their electrons are immobile. “Metallic frustrated magnets have been highly sought after for several decades. They have been predicted to house unconventional superconductivity, Majorana fermions, be useful for quantum computing, and more,” commented Dr. Ali.
Structurally, KV3Sb5 has a 2D, layered structure where triangular vanadium and antimony layers loosely stack on top of potassium layers. This allowed the authors to simply use tape to peel off a few layers (a.k.a. flakes) at a time. “This was very important because it allowed us to use electron-beam lithography (like photo-lithography which is used to make computer chips, but using electrons rather than photons) to make tiny devices out of the flakes and measure properties which people can’t easily measure in bulk.” remarked lead author Shuo-Ying Yang, from the Max Planck Institute of Microstructure Physics. “We were excited to find that the flakes were quite stable to the fabrication process, which makes it relatively easy to work with and explore lots of properties.”
Armed with this combination of properties, the team first chose to look for an anomalous Hall effect (AHE) in the material. This phenomenon is where electrons in a material with an applied electric field (but no magnetic field) can get deflected by 90 degrees by various mechanisms. “It had been theorized that metals with triangular spin arrangements could host a significant extrinsic effect, so it was a good place to start,” noted Yang. Using angle resolved photoelectron spectroscopy, microdevice fabrication, and a low temperature electronic property measurement system, Shuo-Ying and co-lead author Yaojia Wang (Max Planck Institute of Microstructure Physics) were able to observe one of the largest AHE’s ever seen.
The AHE can be broken into two general categories: intrinsic and extrinsic. “The intrinsic mechanism is like if a football player made a pass to their teammate by bending the ball, or electron, around some defenders (without it colliding with them),” explained Ali. “Extrinsic is like the ball bouncing off of a defender, or magnetic scattering center, and going to the side after the collision. Many extrinsically dominated materials have a random arrangement of defenders on the field, or magnetic scattering centers randomly diluted throughout the crystal. KV3Sb5 is special in that it has groups of 3 magnetic scattering centers arranged in a triangular net. In this scenario, the ball scatters off of the cluster of defenders, rather than a single one, and is more likely to go to the side than if just one was in the way.” This is essentially the theorized spin-cluster skew scattering AHE mechanism which was demonstrated by the authors in this material. “However the condition with which the incoming ball hits the cluster seems to matter; you or I kicking the ball isn’t the same as if, say, Christiano Ronaldo kicked the ball,” added Ali. “When Ronaldo kicks it, it is moving way faster and bounces off of the cluster with way more velocity, moving to the side faster than if just any average person had kicked it. This is, loosely speaking, the difference between the Dirac quasiparticles (Ronaldo) in this material vs normal electrons (average person) and is related to why we see such a large AHE,” Ali laughingly explained.
These results may also help scientists identify other materials with this combination of ingredients. “Importantly, the same physics governing this AHE could also drive a very large spin Hall effect (SHE) — where instead of generating an orthogonal charge current, an orthogonal spin current is generated,” remarked Wang. “This is important for next-generation computing technologies based on an electron’s spin rather than its charge.”
“This is a new playground material for us: metallic Dirac physics, frustrated magnetism, exfoliatable, and chemically stable all in one. There is a lot of opportunity to explore fun, weird phenomena, like unconventional superconductivity and more,” said Ali, excitedly. More

A breakthrough in fertility science by researchers from Bristol and Mexico has shattered the universally accepted view of how sperm ‘swim’.
More than three hundred years after Antonie van Leeuwenhoek used one of the earliest microscopes to describe human sperm as having a “tail, which, when swimming, lashes with a snakelike movement, like eels in water,” scientists have revealed this is an optical illusion.
Using state-of-the-art 3D microscopy and mathematics, Dr Hermes Gadelha from the University of Bristol, Dr Gabriel Corkidi and Dr Alberto Darszon from the Universidad Nacional Autonoma de Mexico, have pioneered the reconstruction of the true movement of the sperm tail in 3D.
Using a high-speed camera capable of recording over 55,000 frames in one second, and a microscope stage with a piezoelectric device to move the sample up and down at an incredibly high rate, they were able to scan the sperm swimming freely in 3D.
The ground-breaking study, published in the journal Science Advances, reveals the sperm tail is in fact wonky and only wiggles on one side. While this should mean the sperm’s one-sided stroke would have it swimming in circles, sperm have found a clever way to adapt and swim forwards.
“Human sperm figured out if they roll as they swim, much like playful otters corkscrewing through water, their one-sided stoke would average itself out, and they would swim forwards,” said Dr Gadelha, head of the Polymaths Laboratory at Bristol’s Department of Engineering Mathematics and an expert in the mathematics of fertility.

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“The sperms’ rapid and highly synchronised spinning causes an illusion when seen from above with 2D microscopes — the tail appears to have a side-to-side symmetric movement, “like eels in water,” as described by Leeuwenhoek in the 17th century.
“However, our discovery shows sperm have developed a swimming technique to compensate for their lop-sidedness and in doing so have ingeniously solved a mathematical puzzle at a microscopic scale: by creating symmetry out of asymmetry,” said Dr Gadelha.
“The otter-like spinning of human sperm is however complex: the sperm head spins at the same time that the sperm tail rotates around the swimming direction. This is known in physics as precession, much like when the orbits of Earth and Mars precess around the sun.”
Computer-assisted semen analysis systems in use today, both in clinics and for research, still use 2D views to look at sperm movement. Therefore, like Leeuwenhoek’s first microscope, they are still prone to this illusion of symmetry while assessing semen quality. This discovery, with its novel use of 3D microscope technology combined with mathematics, may provide fresh hope for unlocking the secrets of human reproduction.
“With over half of infertility caused by male factors, understanding the human sperm tail is fundamental to developing future diagnostic tools to identify unhealthy sperm,” adds Dr Gadelha, whose work has previously revealed the biomechanics of sperm bendiness and the precise rhythmic tendencies that characterise how a sperm moves forward.
Dr Corkidi and Dr Darszon pioneered the 3D microscopy for sperm swimming.
“This was an incredible surprise, and we believe our state-of the-art 3D microscope will unveil many more hidden secrets in nature. One day this technology will become available to clinical centres,” said Dr Corkidi.
“This discovery will revolutionize our understanding of sperm motility and its impact on natural fertilization. So little is known about the intricate environment inside the female reproductive tract and how sperm swimming impinge on fertilization. These new tools open our eyes to the amazing capabilities sperm have,” said Dr Darszon. More

Using data from NASA’s Solar Dynamics Observatory, or SDO, scientists have developed a new model that successfully predicted seven of the Sun’s biggest flares from the last solar cycle, out of a set of nine. With more development, the model could be used to one day inform forecasts of these intense bursts of solar radiation.
As it progresses through its natural 11-year cycle, the Sun transitions from periods of high to low activity, and back to high again. The scientists focused on X-class flares, the most powerful kind of these solar fireworks. Compared to smaller flares, big flares like these are relatively infrequent; in the last solar cycle, there were around 50. But they can have big impacts, from disrupting radio communications and power grid operations, to — at their most severe — endangering astronauts in the path of harsh solar radiation. Scientists who work on modeling flares hope that one day their efforts can help mitigate these effects.
Led by Kanya Kusano, the director of the Institute for Space-Earth Environmental Research at Japan’s Nagoya University, a team of scientists built their model on a kind of magnetic map: SDO’s observations of magnetic fields on the Sun’s surface. Their results were published in Science on July 30, 2020.
It’s well-understood that flares erupt from hot spots of magnetic activity on the solar surface, called active regions. (In visible light, they appear as sunspots, dark blotches that freckle the Sun.) The new model works by identifying key characteristics in an active region, characteristics the scientists theorized are necessary to setting off a massive flare.
The first is the initial trigger. Solar flares, especially X-class ones, unleash huge amounts of energy. Before an eruption, that energy is contained in twisting magnetic field lines that form unstable arches over the active region. According to the scientists, highly twisted rope-like lines are a precursor for the Sun’s biggest flares. With enough twisting, two neighboring arches can combine into one big, double-humped arch. This is an example of what’s known as magnetic reconnection, and the result is an unstable magnetic structure — a bit like a rounded “M” — that can trigger the release of a flood of energy, in the form of a flare.
Where the magnetic reconnection happens is important too, and one of the details the scientists built their model to calculate. Within an active region, there are boundaries where the magnetic field is positive on one side and negative on the other, just like a regular refrigerator magnet.
“It’s similar to an avalanche,” Kusano said. “Avalanches start with a small crack. If the crack is up high on a steep slope, a bigger crash is possible.” In this case, the crack that starts the cascade is magnetic reconnection. When reconnection happens near the boundary, there’s potential for a big flare. Far from the boundary, there’s less available energy, and a budding flare can fizzle out — although, Kusano pointed out, the Sun could still unleash a swift cloud of solar material, called a coronal mass ejection.
Kusano and his team looked at the seven active regions from the last solar cycle that produced the strongest flares on the Earth-facing side of the Sun (they also focused on flares from part of the Sun that is closest to Earth, where magnetic field observations are best). SDO’s observations of the active regions helped them locate the right magnetic boundaries, and calculate instabilities in the hot spots. In the end, their model predicted seven out of nine total flares, with three false positives. The two that the model didn’t account for, Kusano explained, were exceptions to the rest: Unlike the others, the active region they exploded from were much larger, and didn’t produce a coronal mass ejection along with the flare.
“Predictions are a main goal of NASA’s Living with a Star program and missions,” said Dean Pesnell, the SDO principal investigator at NASA’s Goddard Space Flight Center in Greenbelt, Maryland, who did not participate in the study. SDO was the first Living with a Star program mission. “Accurate precursors such as this that can anticipate significant solar flares show the progress we have made towards predicting these solar storms that can affect everyone.”
While it takes a lot more work and validation to get models to the point where they can make forecasts that spacecraft or power grid operators can act upon, the scientists have identified conditions they think are necessary for a major flare. Kusano said he is excited to have a promising first result.
“I am glad our new model can contribute to the effort,” he said. More

Researchers at the University of the Witwatersrand in Johannesburg, South Africa, have demonstrated a record setting quantum protocol for sharing a secret amongst many parties. The team created an 11-dimensional quantum state and used it to share a secret amongst 10 parties. By using quantum tricks, the secret can only be unlocked if the parties trust one another. The work sets a new record for the dimension of the state (which impacts on how big the secret can be) and the number of parties with whom it is shared and is an important step towards distributing information securely across many nodes in a quantum network.
Laser & Photonics Reviews published online the research by the Wits team led by Professor Andrew Forbes from the School of Physics at Wits University. In their paper titled: Experimental Demonstration of 11-Dimensional 10-Party Quantum Secret Sharing, the Wits team beat all prior records to share a quantum secret.
“In traditional secure quantum communication, information is sent securely from one party to another, often named Alice and Bob. In the language of networks, this would be considered peer-to-peer communication and by definition has only the two nodes: sender and receiver,” says Forbes.
“Anyone who has sent an email will know that often information must be sent to several people: one sender and many receiving parties. Traditional quantum communication such as quantum key distribution (QKD) does not allow this, and is only of the peer-to-peer form.”
Using structured light as quantum photon states, the Wits team showed how to distribute information from one sender to 10 parties. Then, by using some nifty quantum tricks, they could engineer the protocol so that only if the parties trust one another can the secret be revealed.
“In essence, each party has no useful information, but if they trust one another then the secret can be revealed. The level of trust can be set from just a few of the parties to all of them,” says Forbes. Importantly, at no stage is the secret ever revealed through communication between the parties: they don’t have to reveal any secrets. In this way a secret can be shared in a fundamentally secure manner across many nodes of a network: quantum secret sharing.
“Our work pushes the state-of-the-art and brings quantum communication closer to true network implementation,” says Forbes. “When you think of networks you think of many connections, many parties, who wish to share information and not just two. Now we know how to do this the quantum way.”
The team used structured photons to reach high dimensions. Structured light means ”Patterns of light” and here the team could use many patterns to push the dimension limit. More dimensions mean more information in the light, and translates directly to larger secrets.

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Materials provided by University of the Witwatersrand. Note: Content may be edited for style and length. More

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