8. Hadamard's Three-Lines Theorem: bsky.app/profile/qit-...

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Quantum Toolbox (8): Hadamard's Three-Lines Theorem (1/6)

👏💐Congrats to PhD student Roberto Rubboli who successfully defended his thesis, "Optimization and Additivity of Quantum Relative Entropies"! He was advised by @marcotomamichel.bsky.social‬. Next, he will join the group of Daniel Stilck França at the University of Copenhagen. All the best Dr Roberto!

Meet a CQTian: Tristan Philippe - CQT - Centre for Quantum Technologies For French student Tristan, Singapore’s National Quantum Scholarship supports him to work on theoretical quantum cryptography

"I’m interested in how we create quantum primitives which ensure security of data," says Tristan Philippe, one of the first PhD students to start research at CQT under Singapore's National Quantum Scholarships Scheme 🇸🇬 🎓 Read his interview: bit.ly/3Zc95KK

7. Continuity of the von Neumann Entropy: bsky.app/profile/qit-...

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Quantum Toolbox (7): Continuity of the von Neumann Entropy (1/6)

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However, lower bounds from related results on conditional independence testing in l1 distance show that the complicated structure of our sample complexity is indeed necessary. We also resolve the sample complexity of mutual information testing up to logarithmic factors. (5/6)

The additional structure of our problem allows for a more fine-grained bucketing. An additional obstacle is the simulation of samples from the reference distribution. For small probabilities, we can only do this approximately, introducing correlations and a bias, which requires a new tester. (4/6)

On a technical level, we employ known techniques to reduce the problem to instances of equivalence testing in l2 distance. This requires approximately learning the distribution to create buckets of similar weight, which are tested individually using an instance-optimal algorithm. (3/6)

To decide whether correlations between variables of a tripartite discrete probability distribution share a direct link of causation, we test whether the conditional mutual information is zero or above a threshold. (2/6)

Testing (Conditional) Mutual Information We investigate the sample complexity of mutual information and conditional mutual information testing. For conditional mutual information testing, given access to independent samples of a triple of ra...

We are happy to share our work in classical distribution testing "Testing (Conditional) Mutual Information" (arxiv.org/abs/2506.03894), which was recently accepted at COLT 2025. (1/6)

6. Hoeffding's Inequality: bsky.app/profile/qit-...

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Quantum Toolbox (6): Hoeffding's Inequality (1/7)