Teaching is fun. Today, I have covered elements of the Pauli and Clifford groups. Cutely, at the very same moment when in Cologne, a #Berlin-#Cologne workshop is talking place on the Clifford commutant, triggered by two papers only, arxiv.org/abs/2504.12263, arxiv.org/abs/1712.08628.

I’d like to advertise two cute technical results of today’s paper that may be of independent interest (I hope): A new decomposition of Gaussian unitaries and new bosonic trace distance bounds (the saga of bosonic trace distance bounds never ends! 😍) arxiv.org/abs/2504.19319 1/

New bosonic paper out! Take the covariance matrix of a pure state and count the number of symplectic eigenvalues that are strictly larger than one: this is a powerful non-Gaussian monotone — the *symplectic rank* arxiv.org/abs/2504.19319 1/

🧵 Super excited to finally share our new paper 🎉 Together with the dream team- Lennart Bittel, @jenseisert.bsky.social, Lorenzo Leone, @sfeoliviero.bsky.social - we present a full theory of the Clifford commutant ⚡, a central object in quantum information. ⚛️ 📄 arxiv.org/abs/2504.12263

A complete theory of the Clifford commutant scirate.com/arxiv/2504.1... The Clifford group is ubiquitous in quantum information science, with applications in benchmarking, quantum error correction and learning algorithms. Understanding which operators commute with is a powerful tool.

New paper out today on "Q Thermo with CV systems"! What is the maximum energy that you can extract from a quantum state via Gaussian unitaries only? We solve this problem by establishing a simple, cute formula for the *Gaussian ergotropy*. 1/ arxiv.org/abs/2503.21748