Physicists have demonstrated a bizarre paradox that offers new insights into a unique aspect of quantum mechanics, potentially helping researchers gain a deeper understanding of “exotic” quantum mysteries.
While pursuing a long-sought variant of a paradox that has eluded physicists for decades, an international team says they successfully demonstrated conditions under which photons appear to exist simultaneously in 37 dimensions.
The findings were the focus of a study that appeared last year in Science Advances.
Contextuality and Quantum Oddities
In the phenomenology of quantum mechanics, contextuality describes how the measurement of a quantum system’s properties depends on other factors measured alongside them, thereby providing the “context” for those measurements. Essentially, this means that our reality is anchored to this contextual measurement component, rather than having preexisting values.
This presents a significant challenge to the once-held intuitions of classical physics, which held that the world around us possesses fixed properties and that we experience it as passive observers. A well-known example of the kinds of quantum oddities that hint at this stranger level of reality is quantum entanglement, where measuring the properties of one particle affects the measurements of its entangled companion, regardless of distance.
This odd phenomenon of quantum nonlocality, which Einstein aptly described as “spooky action at a distance,” runs counter to classical ideas in which objects are primarily influenced by their immediate surroundings.
One proof of contextuality in quantum theory involves what are known as Greenberger-Horne-Zeilinger (GHZ) paradoxes, which describe quantum entanglement under conditions in which at least three subsystems, such as particle states, are involved. The predicted outcomes of these so-called GHZ states (named after the three scientists who first described them) fundamentally contradict all local theories derived from classical views.
However, according to the authors of the study published in Science Advances last year, the search for a GHZ-type paradox capable of presenting events in the fewest possible contexts, thereby providing the best evidence of non-classical physics, has eluded scientists for decades.
Pursuing an Elusive Paradox
To overcome this, the researchers began with a fundamental question: what would the smallest number of contexts be to account for all the events described in a GHZ-type paradox? Referring to the sought-after value as the “number of context-cover” (a distinction, the team notes, from a separate value known as the “number of context”), the team argued that this value could potentially be useful in describing GHZ-type paradoxes for two primary reasons.
“First, when transformed into noncontextuality inequalities, a GHZ-type paradox with a lower number of context-cover yields a larger ratio of violation,” the team wrote last year. “Second, to observe a GHZ-type paradox, the number of groups of fundamental event probabilities required is also equal to the number of context-cover.”
Because of this, they conclude that a GHZ-type paradox with the smallest possible number of context cover could offer potentially strong evidence of non-classical phenomena, which could be very useful in quantum computing applications. However, such a strong form of the paradox in question has remained elusive to physicists for close to three decades, an issue which the team sought to address.
Graphing the Mystery
To achieve this, the team developed a unique method for constructing GHZ paradoxes using graphs that satisfied specific criteria, drawing inspiration from the graph-theoretic approach to quantum correlations.
In this approach, researchers employ what are known as exclusivity graphs, which allow them to measure various outcomes, thereby linking the limits of classical-physical phenomena with post-quantum behaviors. In the past, this has proven to be a powerful tool in helping researchers develop a better understanding of the phenomena involving nonlocality and contextuality.
“To date, no direct method has, to the best of our knowledge, been established for studying the GHZ-type paradox via this approach,” the study’s authors write.
“On the basis of this method, we have explicitly constrained a three-context GHZ-type paradox that can be realized with a set of 37-dimensional measurements,” the team reported. Thereafter, the team studied the three-context GHZ-type paradox using a specialized photonic processor, which enabled them to reproduce all the high-dimensional measurement probabilities in the paradox.
Toward Understanding Exotic Systems
Their results, the team says, helped detail the potential of using similar optical systems for such research, as well as the discovery of exotic quantum correlations that serve as the basis for quantum computing applications.
“Our result thus highlights the link between the most exotic quantum correlations and graphs with high degrees of symmetry and may shed light on the search for other strong forms of quantum correlations,” the study’s authors write.
Additionally, they argue that in the future, a potentially promising outgrowth of their research might involve converting the significant non-classicality observed in their three-context GHZ-paradox into a form of quantum advantage, noting that quantum advantage in shallow circuits has already been realized based on contextuality.
“We hope our findings can be used to build even stronger quantum advantages in high-dimensional systems,” the team concludes.
The team’s study, “Exploring the boundary of quantum correlations with a time-domain optical processor,” appeared in Science Advances.
Micah Hanks is the Editor-in-Chief and Co-Founder of The Debrief. A longtime reporter on science, defense, and technology with a focus on space and astronomy, he can be reached at micah@thedebrief.org. Follow him on X @MicahHanks, and at micahhanks.com.