Disordered systems are common, and how entanglement evolves in them can inform quantum computations.
BY DEBDUTTA PAUL
Quantum mechanics differs significantly from the classical Newtonian perspective of explaining the natural world. The phenomenon of quantum entanglement quantifies the stark difference sharply.
Theoretical physicists at ICTS-TIFR have now provided a microscopic explanation of how entanglement evolves in a fully quantum mechanical system. Their paper was published in the journal Physical Review B.
Quantum entanglement
Fundamental particles, like electrons, behave very differently from macroscopic systems, like balls, stones, or even grains of sand. Physicists can describe them using the rules of quantum mechanics only, and conceptually, there are two such rules.
According to one rule, systems of interest evolve following a specific equation. According to another, whenever an observer measures the system’s state, it “collapses” into one of its many special states following a probability law. The second rule creates spooky phenomena like quantum entanglement.
According to these rules, interacting quantum particles can have their properties dependent on each other in ways that a measurement of one particle’s property predicts the others’. For example, electrons have a property called ‘spin’, which can be either up or down. When two electrons are such that their spins are opposite, if one electron is measured to have up-spin, the other must have down-spin. Then, they are said to be entangled.
“Entanglement is fundamental because it quantifies correlations which distinguish what is genuinely quantum from what is classical,” said Sthitadhi Roy from ICTS-TIFR, one of the co-authors. “It describes quantum correlations which cannot be described from classical origins.”
When there are many such quantum particles and they all interact with each other, they can all get entangled. For a physicist, then, it is impossible to describe different parts of the system separately. This natural fact is very different from Newtonian mechanics, which often clumps many particles together and describes them as a composite system. For example, if a bucket of water is divided into two parts by pouring half into another bucket, we can describe the two halves separately. But each half contains many molecules of water. In purely quantum mechanical composites of elementary particles, such clumping isn’t possible due to entanglement.
Entangled systems
Purely quantum mechanically entangled states are surprisingly common. “A classic real-life example of a quantum many-body system around us is the semiconductor chips in our electronic devices,” said Sthitadhi.
In such a quantum clump of matter, changes in particles in one place may affect particles in other locations. So, physicists need to study to what extent different parts of the system are synced or correlated. Entanglement leads to quantum correlation, and the degree of correlation evolves with time. Then, physicists define mathematical quantities that capture the degree of correlation and use them to study the system’s evolution.
One of them is called the ‘entanglement entropy’, which quantifies how much the system is disordered. As the system evolves, the entanglement entropy increases and settles at a fixed value. The disorder is then maximum.
Earlier studies have shown how it evolves in different quantum composite systems. The physicists’ favourite system resembles real-life solids, which contain a lattice of nuclei (containing protons and neutrons) and free electrons that hop around the lattice. If the electrons interact heavily with each other, the entanglement entropy increases rapidly. Physicists understand how.
But, in a system where the spacing between the nuclei is random, the evolution slows down. Such systems are called ‘disordered systems.’
“Most quantum mechanical materials, either found naturally or synthesised in the laboratory, are disordered,” said Sthitadhi. “The most modern quantum devices, such as the quantum processors developed by Google and IBM, can also be disordered.”
Why disordered systems evolve slowly
Physicists know how their evolution slows down, but they don’t understand why. The ICTS researchers have an answer.
In principle, the answer lies in the complicated mathematics of many entangled quantum mechanical states. Certain mathematical quantities contain the answer to all the mysteries, but it’s impractical to calculate them all because of the sheer amount of computation it would need. Moreover, “[it] is an extremely large amount of information, so large that it is effectively useless,” said Sthitadhi.
The duo’s study has pinned down which correlations are useful to describe the evolution of quantum entanglement in a disordered quantum mechanical system.
Since entanglement is a fundamentally quantum mechanical phenomenon and quantum computing uses the dynamics of its evolution, the duo’s insight might help researchers fine-tune how they understand quantum computing.
Moreover, strongly disordered entangled systems can serve as quantum memory devices, said Sthitadhi, because the state of the system stays frozen for a very long time. “Understanding the entanglement dynamics… might shed light on if such systems can indeed be used as quantum memories and how good they will be,” he signed off.
The author thanks Bikram Pain and Sthitadhi Roy for discussions.