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The qudit Pauli group: non-commuting pairs, non-commuting sets, and structure theorems

Rahul Sarkar1 and Theodore J. Yoder21Institute for Computational and Mathematical Engineering, Stanford University, Stanford, CA 943052IBM T.J. Watson Research Center, Yorktown Heights, NYFind this...

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Quantum-optimal information encoding using noisy passive linear optics

Andrew Tanggara1,2, Ranjith Nair2, Syed Assad3,4, Varun Narasimhachar5,2, Spyros Tserkis3, Jayne Thompson5, Ping Koy Lam3,4, and Mile Gu2,1,61Centre for Quantum Technologies, National University...

The Astonishing Behavior of Recursive Sequences | Quanta Magazine

IntroductionIn mathematics, simple rules can unlock universes of complexity and beauty. Take the famous Fibonacci sequence, which is defined as follows: It begins with...

Tilted Hardy paradoxes for device-independent randomness extraction

Shuai Zhao1, Ravishankar Ramanathan1, Yuan Liu1, and Paweł Horodecki2,31Department of Computer Science, The University of Hong Kong, Pokfulam Road, Hong Kong2International Centre for Theory...

Complexity Theory’s 50-Year Journey to the Limits of Knowledge | Quanta Magazine

IntroductionIn the first week of the fall semester in 2007, Marco Carmosino dragged himself to a math class required for all computer science majors...

Dogecoin vs Bitcoin: Key Differences and Similarities

What is Dogecoin? Dogecoin is an alternative coin — more commonly known as an Altcoin — that was established by co-founders Jackson Palmer and Billy...

Does Nothingness Exist? | Quanta Magazine

IntroductionAristotle argued almost 2,400 years ago that a perfect vacuum could never exist. Today, the concept of nothingness figures at least implicitly into almost...

New Proof Shows That ‘Expander’ Graphs Synchronize | Quanta Magazine

IntroductionSix years ago, Afonso Bandeira and Shuyang Ling were attempting to come up with a better way to discern clusters in enormous data sets...

New Proof Threads the Needle on a Sticky Geometry Problem | Quanta Magazine

IntroductionIn 1917, the Japanese mathematician Sōichi Kakeya posed what at first seemed like nothing more than a fun exercise in geometry. Lay an infinitely...

Flow Proof Helps Mathematicians Find Stability in Chaos | Quanta Magazine

IntroductionAs with so much in mathematics, the proof started with coffee. In September 2019, Kathryn Mann of Cornell University visited Kingston, Ontario, to give...

Next BAYC or CryptoPunks? Discover Hot New NFTs to Buy Using Launchpad.xyz

Join Our Telegram channel to stay up to date on breaking news coverage The floor prices for blue-chip NFT collections such as CryptoPunks and Bored...

Why Mathematicians Re-Prove What They Already Know

IntroductionThe first proof that many people ever learn, early in high school, is the ancient Greek mathematician Euclid’s proof that there are infinitely many...

Stacks (STX): What if Bitcoin Had Smart Contracts?

Bitcoin maxis, beware! The Stacks crypto project is here to extend the Bitcoin blockchain beyond its limitations, bringing improved functionality to the world’s largest...

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