Frontiers of Science

Fascinated by the deep and beautiful world of quantum mechanics


Professor, Department of Physics

January 4, 2023


Peculiar “superpositions”

The 2022 Nobel Prize in Physics was awarded to Alain Aspect from the University of Paris-Saclay, France, Dr. John Clauser from the United States, and Professor Anton Zeilinger from the University of Vienna, Austria, for their major contributions to the study of quantum entanglement (also simply called entanglement). This sparked the world’s interest in quantum information science and quantum computing, in which quantum entanglement plays an essential role. This is precisely the field that Professor Mio Murao has been working on.

“My father is a researcher in engineering. He asked me to explain what quantum entanglement was in a way that was easy to understand. I tried, but he got frustrated because he couldn’t quite grasp what I was saying,” Murao chuckles.

Quantum mechanics, which deals with the microscopic world of electrons, photons, and atomic nuclei, is indeed full of strange things that go against our common intuitions. Even Einstein did not fully accept the phenomenon of quantum entanglement, remarking that it was a “spooky action at a distance.” So, Murao has no choice but to say this.

“If you want to explain it in a way to truly understand [quantum mechanics], you have to start with the mathematics of linear algebra. But people don’t seem to like that (laughs). In the end, the superposition principle is the most important and fundamental, making quantum entanglement possible. To properly understand the superposition principle, it is crucial to understand linear algebra and vectors, which brings us back to square one. But these vectors are vectors of complex numbers, which are difficult to imagine and get used to...” Murao's expression is more restrained this time.

In our everyday world, we can simultaneously measure an object's position and momentum (such as velocity) and know their values. This way, we can calculate, for example, the trajectory of a ball thrown by Shohei Ohtani, a player for the MLB Angels in the US. In the microscopic world, however, the position and momentum of a particle cannot be measured at the same time, and it is not possible to retrieve precise information about each. This happens because in quantum mechanics, measuring a superposition state breaks the superposition. Once the particle is measured, it is randomly changed to one of the states consisting of the superposition according to the degree of superposition. The position and momentum are related by a superposition of the other kind for each. This fact and the measurement property lead to a relation called the uncertainty principle. In other words, superposition is a state in which all possibilities that have not yet been realized before the measurement “overlap and exist” as possibilities. It is a very strange state indeed.

There is a famous, if somewhat cruel, thought experiment called “Schrodinger's cat.” A single cat is placed in a box. A poison gas device that is turned on by the decay of radioactive elements is set up so that the cat dies at random probability. You can tell if the cat is dead or still alive by opening the box and looking inside. Now, in a situation where you cannot see inside the box, is the cat inside dead or alive? Common sense tells us, of course, that the cat is either dead or alive, and we simply don't know. However, if we view the cat's state as a superposition in quantum mechanics, the cat is neither dead nor alive. It is in a superposition of two states, alive and dead.

“This is not the same as saying that a cat has a certain probability of being alive and a certain probability of being dead. Nor is the cat alive and dead at the same time. The cat in the box has components of a living state and a dead state but, it is neither dead nor alive. In other words, it's in a superposition.”

A cat that is dead yet alive, a cat that is alive while being dead – it’s not even that... This could be nothing but a superposition.

A particle is a particle, not a wave

“As exhibited by the fact that position and momentum are related by a superposition, we can say that the fundamental principle of quantum mechanics is this superposition principle. People often use a wave analogy to explain superpositions. Although wave properties are being observed, we can’t say that particles are waves. Particles are particles. And they can be in superpositions like waves. Sometimes, the superposition of particles is called a “wave,” and many textbooks explain this as a duality between a wave and a particle. But I feel that is a big misunderstanding, treating waves and particles in equal standing.”

The “double-slit experiment” is used to explain this “wave-particle duality.” There is an electron gun that can fire electrons one at a time. The screen at the end of the muzzle of the gun is marked when the electrons hit it (this is the measurement). Between the electron gun and the screen, a plate with two slits (slim gaps lined up like a “II”) is placed. Now, suppose that electrons are shot continuously from the electron gun in this state. Since the electrons hit the screen through one of the two slits, the screen will probably have a mark on it that looks like a “II,” the same as the slits. However, what is drawn on the screen is a stripe pattern with a gradation of shading like a “III.” This can only be attributed to the fact that an electron passes through two slits at the same time as a wave, creating interference fringes. This is the reason why electrons are sometimes described as waves and sometimes as particles. However, Murao explains that it is not a “wave-particle duality,” but rather “a particle is a particle,” and the superposition of particles passing through different slits is analogically called a “wave.” Such a situation is even harder to imagine than the wave-particle duality, which is already difficult to understand…

“The properties of quantum mechanics are very mysterious when considered by classical analogy and can cause a lot of counter-intuitive things to happen. Quantum entanglement causes the curious property that, in the case of a photon, measuring one of two entangled photons instantly affects the other. However, this phenomenon naturally happens due to the properties of complex vectors with superposition states and is not at all surprising if you follow the rules of quantum mechanical measurement. For me, the quantum world has become so normal that I am starting to feel like there is nothing strange about it, it's just the way it is. If anything, the everyday classical world sometimes seems more like a special situation.”

To us, it is still a mystery, however. So, I would like to challenge myself here and explain quantum entanglement. Let us take the electron as an example. Here are two electrons that are strongly correlated by quantum entanglement (they are in a so-called EPR state). These two electrons have a special superposition: no matter how far apart they are, when the state of one electron is measured, the superposition is broken, instantly inducing a change in the state of the other electron corresponding to the measurement result. It is as if they were twins bound by fate. For example, suppose that one of the two electrons in the EPR state is placed on Earth and the other on the Moon. When the direction of the electron's spin (the angular momentum specific to quantum mechanics) on Earth is measured and determined to be upward (z-axis up), the spin of the other electron on the Moon is instantly determined as downward (z-axis down). Even more surprisingly, when the direction of the electron spin measurement is changed and it is determined to be rightward (upward on the x-axis), the spin of the other electron on the lunar surface is instantly determined to be leftward (downward on the x-axis). It is as if information about the direction and result of the measurement was transmitted from a photon on Earth to a photon on the Moon's surface at a speed exceeding the speed of light! This is quantum entanglement. Of course, there could be no such thing as information transmitted faster than the speed of light. This is why Einstein dismissed quantum entanglement. However, the three Nobel laureates in Physics in 2022 have experimentally proven that Einstein was wrong, and that the phenomenon of quantum entanglement definitely exists. However, quantum entanglement does not transmit information faster than the speed of light. Quantum entanglement creates strong correlations that are impossible in classical mechanics, as measurement can change states faster than the speed of light. However, the measurement results are randomly determined, and the correlated measurement result cannot be obtained without knowing the direction of the measurement, so after all information does not propagate faster than the speed of light.

Why-why Mio

As a child, Murao was called “Why-why Mio.”

“I always wondered about things like “Why does the sky turn blue or red?” I would always ask my parents and my neighbors: “Why? Why?” I was a bit of an “annoying” child, always pestering my parents and neighbors (laughs). Even at school, when I wasn’t convinced by a teacher’s explanation, I would tell them: “I don't understand your explanation.” I'm sure the teachers were rather annoyed with me.”

In high school, she briefly considered becoming a pharmacist but…

“I saw a brochure for a pharmacy school that had a picture of a rat being injected. I'm not good with animals. I can't even touch a rat, let alone inject one,” she thought and gave up. In the end, she went on to the Faculty of Science at Ochanomizu University because “you don’t have to memorize much in physics, so it’s easy.” It was there that she met her fate in quantum mechanics.

“What attracted me was the concept of “superpositions”. It made me think that there is more to the world than what we can perceive with our eyes. I realized that I was only seeing one aspect of the world. This is where I felt the depth of quantum mechanics. It is all so mysterious at first glance, but it is all based on logic. I can derive all the results by logic from a small number of assumptions, and it all makes sense in the end. That's what makes it fun.”

When an answer to the first question of “why” can be found, the answer sometimes leads to another “why”. We take a step forward to solve it, then we hit another “why?” again.

While doing her master's degree, she was looking for a job as a researcher at a company working on quantum devices. However, during her visit to a major company, a researcher told her that if she wanted to do fundamental research, she should go to graduate school. So, she changed courses and enrolled in a doctorate program. Later, when she visited Cambridge, she ran into the same researcher who gave her the advice.

“I'm sure he was also someone who wanted to continue fundamental research, so he told me that if I wanted to do fundamental research, I shouldn't come to his company. In a sense, I owe him a favor. Although I have low self-confidence and get disheartened from time to time, I consider myself really lucky. I have met many people who encouraged me, and I think that's why I am now one of the few surviving women researchers.”

Encouraged she was, even at Harvard University.

“I was having a hard time because everyone seemed really smart. I felt like I was behind, and my research was not going well, either. But one day in the hallway I passed by Dr. Hans Briegel, who is now a world-renowned professor but was a postdoc at the time, and he reassured me. He asked me how I was doing, and I replied something along the lines of, “Not fine. Everyone is so bright and it’s driving me mad.” He said that everyone just seemed smart, but it was just for show,” she laughed. “That comment made me think that I should go my own way and not worry so much about others. People are people. I have to do what I can do, one step at a time.”

Murao has this message for students and women scientists.

“After all, what is important is what you want to do, your instincts. Don't worry about the rest. Think about what you want to do first and foremost. When I go abroad for research and talk to various people, I find that many of them seem to be standing on their own feet. They have been pioneers where no one else has because they wanted to pursue their vision. There are many people like that, and I respect them very much. They don't limit their possibilities. They think about what they want to do and pave the way. It would be nice if there was an atmosphere of encouragement around people, telling them that following their interests was good enough. On the off chance that you fail, you might waste a year or two. But life is long, that much is not a big deal.”

Looking to the Future of Quantum Computing

One such unexplored area that Murao is researching herself is quantum algorithms. This is a historical and creative field, where she is laying the foundations for the computational methods of quantum computers, a technology still in its infancy.

“This is research on what kind of calculations are possible with a quantum computer, how programming should be done, and new algorithms that are unique to a quantum computer. Rather than trying to do something interesting with the current rudimentary quantum computers, which do not perform very well yet, we are mainly doing basic research on what will be possible when superior quantum computers appear in the future.”

The computers we use in our daily lives (called classical computers) and quantum computers work in completely different ways. While classical computers use transistors to represent 0s and 1s (bits) to perform calculations, quantum computers create a superposition of quantum 0s and 1s (qubits) and manipulate these states to perform calculations. Although both have similarities in that programs consist of a sequence of elementary gates, the quantum computer uses commands to create superposition states, quantum entanglement, and other operations that are totally different from those of a classical computer. Quantum computers require new algorithms created from scratch.

“In the case of a quantum computer, a qubit is a quantum system, represented by a complex vector. This complex vector of quantum states is then transformed, and finally, the classical information is extracted by quantum measurement. This is what a quantum computer does. By using superpositions well, it is sometimes possible to perform calculations faster than with ordinary computers. The important thing is to “use them well.” For calculations that don’t do so, it won't make any much difference whether they are done by a classical or quantum computer.”

Finding ways to “use superpositions well” is what quantum algorithm research is all about, and Murao continues to take on the challenge of various new endeavors.

“I am working on an algorithm based on a very new idea called higher-order quantum computation, which few people in the world are working on,” she said. “I am also working on distributed quantum computing, which explores how to connect quantum computers that are far from each other and make them work as one big quantum computer. In distributed quantum computation, we utilize the principle of quantum teleportation, which makes use of quantum entanglement. This research also brings up the topics of space-time and the law of causality, which are exciting and very interesting to think about.”

In addition to such a busy research schedule, Murao is also involved in the development of online educational materials on quantum information technology for the Quantum Academy of Science and Technology of the Q-LEAP Education Program, an endeavor that encourages quantum literacy. The program is designed to teach basic quantum mechanics and quantum information technology to first- and second-year university students from various backgrounds.

“I believe that young people need to be quantum literate. For example, some people say that a quantum computer is an amazing machine that can solve anything, or that a quantum computer is fast because 0 and 1 happen at the same time, but these explanations are in fact wrong. A correct understanding is necessary not only in research but also in business, and I hope that people will not be deceived by overoptimism or simplistic explanations.”

Murao believes that the world of complex vectors describing quantum mechanics is very beautiful.

“If you express phenomena in terms of complex vectors, you naturally get superpositions, and you can create a world that is consistent, closed, and beautiful. The seemingly incomprehensible quantum world can all be explained by simple principles,” she smiles cheerfully. Murao enjoys her work as a researcher.

“It's fun. I’m glad that I have become a scientist and consider myself very lucky.”


※Year of interview: 2022
Interview/Text: Minoru Ota
Photography: Junichi Kaizuka

Professor, Department of Physics
B.S., Physics, Ochanomizu University, 1991; Ph.D., Ochanomizu University, 1996; PD, Harvard University, 1996; Imperial College, UK, 1996-99. 1999, RIKEN. 2001, Associate Professor, Graduate School of Science, University of Tokyo, 2015, Professor, Graduate School of Science, The University of Tokyo.


A warrior wizard on a quest for the computers of the future

May 8, 2023


The diverse stories of the School of Science students

April 3, 2023


Understanding “life” through the lens of physics and statistics

April 3, 2023