Quantum states, specifically bosonic and fermionic Gaussian states, have a significant impact on various fields, including quantum optics, many-body physics, and quantum computing. Researchers have been working to determine the minimum number of copies required to learn an accurate classical description of these states, known as sample complexity. Recent studies have made progress in understanding the optimal tomography of these quantum states, which is crucial for advancing quantum science and technology. The development of quantum computing relies heavily on the understanding of these states, as they play a key role in quantum information theory and quantum chemistry. As quantum computing continues to advance, it is rewriting assumptions about computation and cryptography, making it essential to understand the properties of bosonic and fermionic Gaussian states1. This understanding has significant implications for the development of secure cryptographic systems and the future of computation, making it a critical area of research for practitioners in the field.