Quantum mechanics is undergoing its second revolution with the exciting advent of several technologies like quantum computing and quantum cryptography. These technologies are slowly being implemented around the world and are impacting the development of new information technologies. For example, quantum computing is expected to be capable of breaking RSA encryption. At Austin AI, we are aware of these paradigmatic changes and look forward to adapting, implementing, and understanding these cutting-edge advancements, ensuring that our solutions remain at the forefront of the industry. To achieve this, we dive into the principles of quantum mechanics and explore how they lead to the fundamental building blocks of quantum technologies. As part of a series of blogs, we will discuss key concepts of quantum mechanics and how they contribute to the development of quantum information.
Fortunately, many applications of quantum theory, such as quantum computing, do not require extremely dense mathematics. However, quantum physics is conceptually intricate, leading to many misconceptions over time. Thus, before discussing the superposition principle, we’ll provide a brief overview of the theory to set the stage.
⇒ It is a scientific theory. — We cannot emphasize this enough. Due to the rapid spread of misinformation and the misuse of the word “quantum” in various contexts, the status of quantum theory is often misunderstood. The first problem is the common confusion between the concepts of “theory” and “hypothesis.” In physics and other disciplines, a “theory” refers to a well-substantiated organization of scientific knowledge.
Theories can be scientific or not. For instance, string theory is a theory, but it is not a scientific one because it cannot be disproved. On the other hand, general relativity and quantum mechanics are scientific theories, which means they can be disproved. This might sound strange, but the essence of a scientific theory is that it must always allow for the possibility of being disproved. The best we can hope for from a theory is that it doesn’t fail when tested. This is the case with quantum theory. As far as we know, based on numerous experiments (many of which are designed to disprove aspects of the theory), it has not failed.
⇒ Why is quantum theory needed? — At the end of the 19th century, physics seemed complete. Many physicist believed that what remained was just the fixing of specific issues and pathologies of the theories. However, it became clear that the everyday phenomenon called thermal radiation—which occurs in anything with a temperature—could not be explained using classical physics (physics before Einstein’s relativity and quantum mechanics, basically). To address this, Max Planck (the “father” of quantum theory) came out with the idea of “energy quanta” which gave an elegant and simple solution to the problem. In the following years, renowned physicists such as Werner Heisenberg, Erwin Schrödinger, Louis de Broglie, and Albert Einstein, among other great minds, developed the theory into a form very similar to the one we have today.
⇒ The quantum revolutions. — At the invention, consolidation and success of quantum physics, the first quantum revolution took place with the invention of transistors, lasers, atomic clocks, MRI imagers etc. All of this with the help of the recently invented and developed quantum mechanics. Now, the second quantum revolution is taking place in front of our eyes. After the experimental confirmation of quantum entanglement, applications using it as a resource started developing, now we have the first commercial quantum computers and quantum communication and cryptographic devices.
The basic ingredient of this second quantum revolution is quantum information. To understand it and how it has a different or augment nature with respect to classical (conventional) information, let us first dive into the superposition principle.
This principle is one of the basic features of quantum physics, it simply asserts that if two states are physically valid, then their addition is valid too. We call this addition law quantum superposition.
To exemplify the superposition principle, consider the paradigmatic example of a particle in a box. The following figure shows two closed boxes and one red ball somewhere inside, then, we open the boxes to realize that the ball is inside Box 1.
According to classical physics, the only situation possible is that the ball was already inside in Box 1 before we opened it; we just didn’t know it. There is no mystery here.
Now, if we think about the ball as a quantum particle so that quantum physics come into play and opening the box means that we are measuring the ball’s location, there is another possible situation:
The location of the ball is not determined before the measurement; it’s location value does not exist prior the measurement.
⇒ The act of measuring. — As weird as it sounds, the location of the ball “does not exist” before we open the boxes. When we open them and look inside, the act of measuring forces nature to determine the location of the ball. This phenomenon is usually known as wave function collapse. If you think this is very strange, you are right, it is. However, this interpretation of what is happening is perfectly valid according to the experiments, and is a core component of quantum physics. Nonetheless, and as science usually do, this interpretation is still under debate.
⇒ What is the wave function? — In quantum physics, there is a nicely separation of what we observe and the information that dictates how such observations behave on each physical system (the system’s state). This information is packaged in a vector usually called “wave function” (simply because it looks like a wave in many cases). If you are familiar with Natural Language Processing, such packaging can be thought as the features defining a word. The word is the name of the system’s state and the features are the information within. This similarity can be extended further, as the wave function vector also carries probabilistic information, though in a slightly different form called probability amplitude.
⇒ What triggers the collapse and what does it mean?. — Collapsing the wave function means that immediately after the measurement, the wave function is “narrowed down” to the value you just measured, which appears as a “collapse.” This stems from the fact that if you look inside Box 1 immediately after the first measurement, the ball is still there and had a determined location before you looked inside again. Hence, there must be a new wave function compatible with this observation. Thus, we conclude that the state of the system has changed due to the measurement.
⇒ Wave function collapse is not as crazy as you may think. — Collapse also exists in conventional probability theory, it is called statistical collapse. In fact, it is not a big deal. After measuring a system, one gains information about its state, and the probability distribution (which describes our knowledge about the system) is updated accordingly. However, the difference with quantum probability is that the value of the observable does not exist prior to measurement.
⇒ How we should NOT interpret quantum superpositions. — It is common to read or hear that quantum mechanics “predicts” that an object can be in two places at the same time. This is a misunderstanding of the superposition principle; nobody has ever observed a ball being in two places at the same time. In the example with the ball, regardless of whether its location is determined or not before opening the boxes, the ball always appears in only one of them. A superposition of two locations really means that the ball’s quantum state somehow has “presence” in both boxes BEFORE measuring.
⇒ How do we know if the location is determined or not before opening the box?. — As you may notice, in this example it doesn’t matter if the location of the ball is determined or not before the measurement. Unfortunately, it is hard to push this example further to show how we can distinguish between both situations. Nevertheless, it is worth mentioning that it is possible.
Another paradigmatic example of quantum superposition is the famous Schrödinger’s cat. In this thought experiment, a cat is placed in a box with a device that can kill the cat with a certain probability. The device is triggered by a quantum event, so the cat is in a superposition of being dead and alive. Similar to the particle in a box, this example is often misinterpreted, with claims that the cat is alive and dead at the same time.
Schrödinger’s cat is historically significant because it was originally conceived to explore the limitations of quantum mechanics when objects become too large. Mentioning this famous thought experiment is essential when discussing quantum superpositions. It is worth pointing out that part of the limitation involves defining unambiguously what it means to be dead and alive physically, which is a profound and philosophical question.
The superposition principle explained above is basically the key ingredient that brings information beyond conventional. It brings new and powerful degrees of freedom to the arena, so communication and computing can be re-engineered in novel ways.
⇒ Beyond bits. — To grasp how quantum information goes beyond classical information, let us first review what we mean by classical information. Information in computers and smartphones is stored, communicated, and processed in the form of bits, which can be either 0 or 1. This is the basic building block of classical information. On the other hand, quantum bits, or more popularly known as qubits, are the basic building blocks of quantum information. Qubits can be 0 or 1, but similar to the particle in the box, quantum mechanics also allows for quantum superpositions of “0” and “1”.
The figure below schematizes what a qubit is.
⇒ Statistical superpositions. — When describing bits, we also consider situations where we don’t know their value, this is, we have uncertainty. They have a determined value; we just don’t know it. This situation is represented by the blue line connecting “0” and “1.” Points on this line represent situations where we only have probabilities. For example, a bit with a 90% probability of being “0” and a 10% probability of being “1” is represented by a point on the blue line closer to “0” than to “1.” This situation is called statistical superposition. These situations are useful, for example, to describe scenarios where imperfections cause errors in conventional computers. Bits can be flipped with some probability, causing an error.
⇒ Quantum bits as augmentations of bits. — To add quantum superpositions and construct a qubit, the line describing a bit can be augmented with a sphere around it. The bit remains inside, and the sphere describes the superpositions allowed by quantum mechanics. This sphere is not only schematic; in fact, the true augmentation is a sphere called the Bloch sphere. This sphere adds new degrees of freedom to work with, specifically, it adds two angles. To grasp how this is interesting, consider that a conventional bit (for which we know its state perfectly with no uncertainty) can only occupy “0” or “1.” In contrast, a qubit (with a perfectly known state) can have an infinite number of states, described by two real numbers (the two angles).
It might not be entirely clear yet how these angles enhance communication and computing, but a central point to understand is that qubits are “bigger” than bits. They provide more “space” to work with, allowing for greater complexity and capability in quantum computing and communication. Consider the following example that uses this extra space.
⇒ Basic example of quantum encryption. — As mentioned, there is a bit “inside” the qubit (the blue line) and it can be oriented in any direction (not only from north to south, as depicted). When measuring, the wave function will collapse only if the measurement is not aligned with the bit’s orientation. Therefore, to recover the value of the bit stored in the qubit, one must measure it in a specific direction.
There is a protocol called quantum bit commitment that exploits this fact. In this protocol a qubit is communicated from a sender to a receiver. If the qubit arrives without being intercepted, the sender can then reveal the orientation of the bit (the blue line) to the receiver. The receiver then measures the qubit in the specified direction and retrieves the bit value.
If an eavesdropper intercepts the qubit and measures it without knowing the correct orientation, they are likely to choose an incorrect measurement direction. This incorrect measurement will collapse the qubit’s wave function, effectively erasing the original bit information.
More complex encryption protocols, such as BB84 encompass quantum encryption. These methods use laws of nature to do the job, instead of just mathematical algorithms that can be broken with quantum computing.
There are other toy protocols that use a single qubit, such as quantum random number generation and quantum superdense coding, which harness the power of nature for our needs. Nevertheless, the most exciting protocols and applications become possible only when utilizing many qubits.
Quantum mechanics is an exciting field that has greatly expanded our imagination and opened up entirely new avenues for engineering information technologies. The starting point for these advancements is the revolutionary way in which information has been rethought by harnessing quantum effects as a resource. This rethinking of information at the quantum level has led to breakthroughs in quantum computing, quantum cryptography, and quantum communication. Quantum computing, for instance, promises to solve complex problems that are currently intractable for classical computers, from simulating molecular structures to optimizing large-scale systems.
These advancements are not just theoretical; they are actively being pursued and developed by researchers and engineers around the world. The implications for industries such as medicine, finance, and logistics are profound, potentially leading to innovations that can transform our everyday lives.
⇒ Final thoughts. — As an AI company dedicated to advancing information technologies—such as financial services, chatbots, predictive models, and more—we are committed to staying at the forefront of emerging innovations. We are particularly interested in new approaches to constructing IT solutions that leverage the latest developments in quantum technologies. By integrating these cutting-edge advancements, we aim to deliver state-of-the-art solutions and remain competitive in an ever-evolving technological landscape.
We want to keep this conversation going in a series of blogs. There are exciting topics waiting to be discussed, such as quantum entanglement, quantum teleportation, quantum computing and its applications, and some basic tools used in these fascinating fields.
