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An archive of data science, data analytics, data engineering, machine learning, and artificial intelligence writing from the former Towards Data Science Medium publication.

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When 1+1≠2: How Quantum Physics Broke the Laws of Statistics

12 min readMay 3, 2023

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Statistics is a core pillar of data science, yet its assumptions are not always fully tested. This is exacerbated by the rise of quantum computing, where even statistical axioms can be violated. In this article, we explore just how quantum physics breaks statistics, and uncover ways to understand it using data science analogies.

2022’s physics Nobel came down to doing coin-flips, and finding out that quantum physics violated the basic laws of statistics (background: Dan Dennis, coin 3D model: hyperionforge, combination by author)

Let’s play a coin-toss game: toss three coins, and try to have them all land differently. This is a seemingly impossible task, because no matter how rigged a coin is, it can only have two sides. There simply aren’t enough possibilities for all three tosses to land differently.

Yet, with the power of quantum physics, such an impossible feat can be achieved statistically: three coin tosses can all land differently. And the reward for winning? 2022’s Nobel Prize in Physics, which was awarded to Alain Aspect, John Clauser, and Anton Zeilinger on 2022-10-04.

According to nobelprize.org, their achievements were

“for experiments with entangled photons, establishing the violation of Bell inequalities and pioneering quantum information science.”

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TDS Archive
TDS Archive

Published in TDS Archive

An archive of data science, data analytics, data engineering, machine learning, and artificial intelligence writing from the former Towards Data Science Medium publication.

Tim Lou, PhD
Tim Lou, PhD

Written by Tim Lou, PhD

Data Scientist @ TTD | ex Researcher @ Berkeley/LBNL | Particle Physics PhD @ Princeton | Podcast @ quirkcast.org