Measurement in quantum mechanics

In quantum physics, a measurement is when we test a system to get a number result. Quantum theory gives us the chances of different outcomes, not exactly what will happen.

To find these chances, we use a quantum state, which describes the system, with a math rule called the Born rule. For example, a tiny particle like an electron can be described by numbers. Using the Born rule, we can find the chances of where the electron might be when we look for it. The theory can't say for sure where the electron will be, only the chances.

Measuring a quantum system usually changes its state. This idea is important in quantum mechanics. The math for this was developed in the 20th century using linear algebra and functional analysis. Quantum physics has been very useful in many areas.

There are also discussions about what measurement really means. Different interpretations of quantum mechanics try to solve this.

Mathematical formalism

Main article: Canonical quantization

Further information: Dirac–von Neumann axioms

In quantum physics, a measurement is a way to test a system and get a number. One important idea is that quantum theory gives us chances, not certain answers.

To find these chances, we use a special description of the system (its quantum state) together with a math rule for the measurement. This helps us know what might happen when we measure something tiny in the quantum world.

History of the measurement concept

The "old quantum theory"

Main article: Old quantum theory

The old quantum theory is a group of ideas from 1900 to 1925, before modern quantum mechanics. It was not complete, but it tried to fix problems in classical mechanics. Important work included Max Planck’s study of blackbody radiation, Albert Einstein’s work on the photoelectric effect, and Niels Bohr’s model of the hydrogen atom.

The Stern–Gerlach experiment, done in 1922, showed that quantum measurements can have only certain results. In this experiment, silver atoms were passed through a magnetic field. The atoms landed in specific spots on a screen, showing that their spin was “quantized.”

Transition to the "new" quantum theory

In 1925, Werner Heisenberg published a paper that helped shape modern quantum physics. He focused on what could be observed, like the light frequencies atoms absorb or emit.

The uncertainty principle began here. It says we cannot know both an electron’s position and speed at the same time exactly. Later, others gave this principle a precise mathematical form.

From uncertainty to no-hidden-variables

Main articles: EPR paradox, Bell's theorem, and Bell test

Some wondered if quantum mechanics was just an approximation and if there were “hidden variables” that would let us predict more. Bell’s theorem, published in 1964, showed that certain hidden-variable ideas do not match what we see in experiments. Tests since then have supported quantum mechanics.

Quantum systems as measuring devices

The Wigner–Araki–Yanase theorem shows that saving energy limits how well we can measure some things in quantum systems.

Decoherence

Main article: Quantum decoherence

When a quantum system interacts with its surroundings, it can lose its special quantum features. This is called decoherence. It is important in quantum computing, where keeping systems isolated helps maintain their quantum properties.

Quantum information and computation

Quantum information science studies how we use quantum physics to work with information in new ways. Knowing how we measure things in quantum physics is very important for this.

Quantum circuits are a way to do calculations using quantum physics. In these circuits, special steps called quantum gates are used, and then measurements are made to get the results. These circuits work with tiny parts called qubits.

Measurement-based quantum computation is another way to do calculations, where the answer is found by measuring the system. Quantum tomography is a way to learn about the state of a quantum system by looking at the results of many measurements. Quantum metrology uses quantum physics to make very exact measurements, like in experiments that find very small changes.

Laboratory implementations

In the early days of quantum physics, scientists used simple tools like watching light patterns and listening to clicks from special counters to study tiny particles. These tools helped them understand how particles behave.

One famous experiment is the double-slit experiment. In this experiment, scientists shine light or send electrons through two narrow openings. This shows how particles can act like waves. Today, scientists use very sensitive tools to detect single particles, helping them learn more about the strange behavior of very small things.

Interpretations of quantum mechanics

Main article: Interpretations of quantum mechanics

Scientists agree that quantum physics works, but they still discuss what it means. They often talk about how we understand measuring something in quantum physics. One big question is whether the results we see when measuring are truly random or if there is a hidden process causing them. Different ways of thinking about these questions are called "interpretations" of quantum mechanics.

Some interpretations suggest measurement is an approximation of a deeper process. Others see quantum states as information about systems, meaning changes in these states are updates in our knowledge. There is no agreement yet on which approach is best.