Coherence: An Invitation to Explore the Quantum World

The theme of this year’s art competition is Coherence. Coherence represents the most fundamental prerequisite for exploring the quantum world. Yet, like other themes that QNS has addressed in past competitions—such as the quantum world itself, spin, or qubits—coherence remains a difficult and unfamiliar concept.

The QNS Art Competition aims to reinterpret and recompose quantum concepts through art. Through the texts we present, we hope to offer a small guide that helps artists understand the idea of coherence and expand it through their own perspectives and modes of expression. To that end, the Center for Quantum Nanoscience (QNS) has prepared three texts.

The first text provides a scientific explanation of coherence. It introduces the definition of coherence, its physical interpretation, and its importance, using examples that even general audiences can follow.

The second and third texts are part of the “Seodang Dog’s Musings” series. As the old Korean proverb says, “Even a dog at a village school can recite poetry if it stays for three years,” this series explores how non-scientists—who have spent more than five years working alongside quantum physicists—have come to understand and reinterpret coherence. Rather than focusing on explaining coherence, this series shares different interpretations of coherence from artistic and social perspectives. We hope these brief texts will help artists discover new ways of seeing, new directions, and new meanings in “coherence.”

We look forward to seeing every participant express their own coherence in their own artistic language and perspective.

Quantum mechanics’ three core concepts—superposition, entanglement, and coherence—are closely related, yet they describe different physical objects and operate at different conceptual levels. Among them, coherence is the most fundamental concept and refers to the preservation of phase. Without coherence, neither superposition nor entanglement can exist. Only when coherence is maintained can a system exhibit the seemingly magical feature of a superposition of basis states—where a “single particle” exists in multiple states “simultaneously.” Furthermore, when such a superposition extends across multiple particles in an inseparable form, it is called entanglement. In other words, entanglement is a condition in which two or more particles are bound together as a single quantum state. If coherence is destroyed by environmental influence—decoherence—entanglement is destroyed and superposition collapses into a mixed state, ultimately bringing the system back to the familiar laws of classical physics.

If you look up “coherence” in a Korean English dictionary, it is often translated as “consistency.” The word comes from co + haerere, where co is a prefix meaning “together,” and haerere means “to stick” or “to cling.” Thus, etymologically, coherence can be understood as a state in which multiple elements are bound together in a consistent manner. In everyday conversation or logical argument, coherence is used to indicate that statements or reasoning are connected consistently, resulting in clarity. When such everyday terms are introduced into physics, they are defined mathematically within specific physical contexts, but their core meaning does not change substantially. The concept of coherence was originally introduced to understand and explain the wave nature of light. For example, if there are waves with a fixed frequency, wavelength, and amplitude, and if—as in Figure 1—the waves change together in the same form, constructive interference occurs and the wave can be strongly amplified. This is the fundamental principle behind lasers. In this sense, when waves align so that they “stick together” (co-herence)—the term “coherence” is used; and in Korean, it is translated not as “consistency” but as “coherence”.

However, in wave physics, coherence is defined more generally as the property that the phase difference between two waves remains constant—that is, it does not change with time or position. Intuitively, the phase difference can be understood as the degree to which the shapes of the waves are shifted relative to each other. In this sense, Figure 1 illustrates coherent waves with no phase difference, while Figure 2 shows coherent waves with a phase difference.

Coherence is a necessary condition for interference fringes to appear in the double-slit experiment with light. The appearance of an interference pattern on the screen in Figure 3 implies that, as in Figure 4, the relative phase between the two waves is maintained consistently in both time and space.

The concept of coherence introduced through wave physics is extended into quantum mechanics. In quantum mechanics, physical systems such as light or electrons are described by quantum state |ψ⟩. To describe the simplest quantum system, a qubit, two basic states (|0⟩ and |1⟩) are needed. For instance, an electron may have two states: spin up and spin down. In a classical case, this is analogous to describing the state of a coin using heads and tails. A pure quantum state can be written as a superposition of the two basis states as follows:

Here, α and β are complex numbers. Complex numbers have real and imaginary parts and can represent α and β as arrows (vectors) on a two-dimensional plane spanned by the real and imaginary axes. As shown in Figure 5, this plane provides three independent pieces of information: the magnitudes of |α|and |β|, and the angle φ (the phase) between the two vectors.

According to the Copenhagen interpretation of quantum mechanics, the probabilities of finding a quantum state in |0⟩ and |1⟩ are proportional to |α|2 and |β|2, respectively. In addition, the angle φ between α and β contains extra information corresponding to “phase” in wave physics. When the phase φ remains fixed and does not change, it is called a coherent state.

However, such coherence is fragile and can be easily destroyed by the influence of the surrounding environment; this is called decoherence. The environment—air molecules, thermal vibrations, electromagnetic fields, and so on—never stays still and continually fluctuates and perturbs the system’s energy and phase in subtle, random ways. As a result of these random environmental influences, the phase φ discussed in Figure 5 begins to vary unpredictably. For example, if one fixes α and represents random phase fluctuations relative to it, the situation can be visualized as in Figure 6. Consequently, when averaged over time or over many realizations, the phase information (the interference terms) is washed out and effectively disappears.

This process of decoherence can also be understood through the double-slit experiment shown in Figure 3. This experiment applies not only to light but equally to matter waves, such as electrons. To make the idea more intuitive, let us replace electrons with Sun Wukong. At the first slit S0, Sun Wukong clones two perfectly identical —i.e., “coherent”—copies of himself and sends one to slit S1 and the other to S2. These two “coherent” Sun Wukongs meet again on the screen, producing constructive and destructive interference and forming an interference pattern (Figure 7). Now consider the case where environmental influence is present. Suppose that, while traveling along their respective paths, the two Sun Wukongs encounter different monsters and fight them. The Sun Wukong passing through slit S1 and the one passing through S2 fight different monsters, ending up with different injuries and different dirt and grime on their bodies. In quantum-mechanical experiments, the measurement must be repeated many times in order to confirm that the extracted average is meaningful. But because the monsters they encounter and the dirt accumulated varies between experiments the two Sun Wukongs reaching the screen can no longer maintain a “coherent” state with a stable phase relationship. In the end, they fail to produce an interference pattern (Figure 8), and this is a metaphorical explanation of environment-induced decoherence.

From the perspective of an experimental observer in the laboratory, decoherence can be viewed as a physical process in which a pure state—where quantum superposition is maintained—is transformed into a mixed state described by classical probabilities. Strictly speaking, however, the total quantum system including the environment still preserves coherence. The phase information is not destroyed; rather, it is simply “transferred” from the system to the environment. Because we lack the ability to measure or control the vast environment in detail and therefore observe only the qubit system, we interpret this leakage of information from the system into the environment as “a loss of information (i.e., the system has become a mixed state).”

While environmental effects generally hinder the maintenance of quantum phenomena, in the field of quantum sensing, they become a powerful advantage. If a quantum system prepared in a superposition with a well-defined phase is placed into an “unknown environment,” interactions with that environment change the system’s phase relation. The phase shift itself then encodes highly precise information about the environment, effectively turning the quantum system into an ultra-sensitive sensor. Because quantum phases respond sensitively even to extremely small environmental perturbations, this enables ultra-high-resolution detection and imaging. Moreover, coherence allows the initial state of the sensor to be defined clearly, making it easier to infer environmental properties by tracking the changes backward. In practice, atomic clocks and gravitational-wave sensors achieve extraordinary precision by exploiting such quantum coherence. Going further, quantum biology has proposed that coherence may play an important role even in ecological systems. For example, it has been suggested that migratory birds navigate by sensing Earth’s magnetic field through quantum coherence in proteins in their eyes, and attempts are underway to develop next-generation magnetic-field sensors that mimic this biological mechanism.

If a single quantum system serves as an excellent sensor, then two or more quantum systems that maintain coherence with one another can enable powerful quantum computation. A classical computer bit can be either 0 or 1, but a qubit can exist simultaneously in a combined state of 0 and 1 thanks to superposition. Quantum coherence preserves the phase relationships between these states, allowing the superposition to persist across space and time. Instead of operating through simple bit-by-bit manipulation, quantum computing performs operations on the entire set of components of the wavefunction. The key technological challenge is securing a sufficiently long coherence time so that coherence is not lost and errors do not accumulate during computation.

From this perspective, quantum coherence is a precious quantum resource in modern physics. In economics, something qualifies as a resource only if it possesses both scarcity and utility. Quantum coherence satisfies both criteria. Creating coherent states requires extremely delicate techniques, making them difficult to obtain, and in natural conditions they tend to disappear rapidly (scarcity). Yet while coherence is maintained, a quantum computer can outperform even supercomputers (utility).

Everyday objects such as coins or dice are like “discharged batteries”—they are in incoherent states with no usable energy left. When physicists use lasers and ultralow-temperature techniques to create a superposition state in which a coin’s heads and tails exist simultaneously, it is like recharging a battery at great expense. Fueled by this charged energy called “coherence,” a quantum computer races at extraordinary speed toward the destination we call the correct answer. In other words, when we painstakingly “earn” the currency of the quantum world (coherence) using real-world equipment, we can then spend that currency to purchase rare and valuable goods such as ultrafast computation or precision measurement. Recent research in quantum thermodynamics has further revealed that there is an additional form of “work” that can be extracted only from coherent states, and that this plays a role analogous to thermodynamic free energy. Ultimately, the essence of quantum technology lies in preventing this precious fuel from leaking out by sealing the tank well and consuming it as efficiently as possible to extract the highest performance.