*Majorana constellations of some of the most Quantum States in various Dimensions.Courtesy: Luis L. Sanchez Soto.*

Investigators
develop a method to determine how quantum the state of a system is.

Large
objects, such as baseballs, vehicles, and planets, behave in accordance with
the classical laws of mechanics formulated by Sir Isaac Newton. Small ones,
such as atoms and subatomic particles, are governed by quantum mechanics, where
an object can behave as both a wave and a particle.

The
boundary between the classical and quantum realms has always been of great
interest. Research reported in AVS Quantum Science, by AIP Publishing, considers
the question of what makes something “more quantum” than another — is there a
way to characterize “quantumness?” The authors report they have found a way to
do just that.

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

Rather
than proposing a scale whose values would be associated with the degree of
quantumness, the authors of this study look at extrema, namely those states
that are either the most quantum or the least 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 most classical states, but what about the
most quantum states?'” he said.

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

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

The
investigators looked at several ways that other scientists have explored
quantumness and considered the Majorana constellation for each way. They then
asked what the most evenly distributed set of points on a sphere for this
approach is.

As
Sanchez-Soto and his colleagues considered the question of quantumness, they
realized it was a mathematical project “of immense beauty,” in addition to
being useful.