Thank you Zoltan! 🙂

Huge thanks to my co-authors for this fantastic collaboration — @francescoannamele.bsky.social, Lennart Bittel, @jenseisert.bsky.social, Vittorio Giovannetti, @ludovicolami.bsky.social, Lorenzo Leone, and Salvatore F. E. Oliviero! 🚀

Huge thanks to my coauthors, Lennart Bittel, @jenseisert.bsky.social, Marco Fanizza, @vishnu-psiyer.bsky.social, Junseo Lee, Lorenzo Leone, @francescoannamele.bsky.social , and Salvatore F. E. Oliviero.

research.google/programs-and...

I’m honored for this support and grateful to all my collaborators who have made this research journey so exciting. I look forward to continuing my work in quantum information and using the fellowship to broaden my horizons!

It was a great collaboration with Marco Fanizza, Vishnu Iyer, Junseo Lee and Francesco Anna Mele -- mostly entirely done over the past few months on a Whatsapp group that, due to the different time zones of our 3 different continents, was basically constantly active with new insightful messages. 😁

All operations in the protocol are experimentally friendly for current photonic platforms, and the protocol has the nice feature that we can trade more input probe energy for lower sample complexity. 🔦

Now I’m heading to Cologne for the “Clifford Commutant” workshop (quantum-randomness.com/clifford-wor...), organized by Markus Heinrich, Xhek Turkeshi, and David Gross, where our Berlin team will have the chance to present our recent paper: arxiv.org/abs/2504.12263. 🇩🇪

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We hope these results contribute to the toolbox of anyone working with Clifford circuits 🧰.

Thanks again for the wonderful collaboration to my amazing collaborators Lennart Bittel, @jenseisert.bsky.social, Lorenzo Leone, @sfeoliviero.bsky.social. 💪

We’re very happy to receive feedback! 👍

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💥 Applications abound:
• Complete characterization of measurable magic measures 🧮
• Design of optimal stabilizer property testing strategies 🎯
• A new operational interpretation of stabilizer entropy 🔍, and more!

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📐 We also introduce a graphical calculus tool to diagrammatically manipulate and visualize the elements of this new basis 🎨.

Perfect for hands-on calculations: It allowed us to save lots of writing 📚, as many pages of analytical calculations became just a few diagrams 😉.

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This new "Pauli-sum" basis is intuitive and computationally friendly 💻.

It’s (gracefully) generated by products of:
• Permutation operators (which generate the commutant of the unitary group) 🔄
• Just three additional operators 🔑

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🔧 In our work, we give a full description of the commutant for arbitrary n (qubits) and k (tensor powers):

- An explicit orthogonal basis 🧮

- The exact dimension of the commutant 📏

- A new, compact, and easy-to-manipulate basis formed by isotropic sums of Pauli operators 🔀