A mathematical project of “Great Beauty”

Majorana constellations of some of the most quantum states in various dimensions. Credit: Luis L. Sánchez Soto

Investigators develop a method for determining how quantum the state of a system is.

Large objects, such as baseballs, vehicles, and planets, conform to the classical laws of mechanics formulated by Sir Isaac Newton. Small ones, such as atoms and subatomic particles, are driven by quantum mechanics, where an object can behave like a wave and like a particle.

The boundary between the classical and quantum spheres has always been of great interest. Searches reported in AVS Quantum Science, by AIP Publishing, examines the question of what makes one thing “more quantum” than another – is there a way to characterize “quantumism?” The authors report that they have found a way to do this.

The degree of quantism is important for applications such as quantum computing and quantum sensation, which offer advantages not found in their classical counterparts. Understanding these advantages requires, in turn, an understanding of the degree of quantism of the physical systems involved.

Instead of proposing a scale whose values ​​would be associated with the degree of quantum, the authors of this study look at the extremes, that is, those states that are either more quantum or less quantum. Author Luis Sanchez-Soto said the idea for the study came from a question posed at a scientific meeting.

“I was giving a seminar on this topic when someone asked me the question, ‘You guys in quantum optics always talk about the more classical states, but what about the more quantum states?’ “” Tha ai.

It has long been understood that so-called coherent states can be described as almost classical. Coherent states occur, for example, in a laser, where light from multiple photon sources is in phase making them less of a quantum of states.

A quantum system can often be mathematically represented by points on a sphere. This type of representation is called the Majorana constellation and for coherent states, the constellation is simply a single point. Since these are the smallest quantum of states, the more quantum ones would have constellations that cover most of the sphere.

Investigators observed several ways in which other scientists have explored quantum mechanics and considered the Majorana constellation for each mode. They then asked what is the most distributed set of points in a sphere for this approach.

As Sanchez-Soto and his colleagues considered the issue of quantumism, they realized that it was a mathematical project “of extraordinary beauty,” in addition to being useful.

Reference: “Extreme quantum states” by Aaron Z. Goldberg, Andrei B. Klimov, Markus Grassl, Gerd Leuchs and Luis L. Sánchez-Soto, 17 November 2020, AVS Quantum Science.
DOI: 10.1116 / 5.0025819

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