This paper investigates the task of quantum state tomography, which involves reconstructing a quantum state from measurement data. The authors focus on continuous variable (CV) systems, which are characterized by infinite-dimensional Hilbert spaces, and explore the efficiency of tomography algorithms in these systems. They find that the minimum number of copies required for achieving an $\varepsilon$-approximation in trace distance scales as $\sim \varepsilon^{-2n}$, where $n$ is the number of modes, which is significantly more inefficient compared to finite-dimensional systems. Specifically, for energy-constrained pure states, the optimal sample complexity is established, revealing the extreme inefficiency of CV quantum state tomography. To address this inefficiency, the authors investigate more structured classes of quantum states that can be efficiently tomographed. They prove that Gaussian states, a class of states with physically interesting properties, can be efficiently learned using experimentally feasible measurements such as homodyne and heterodyne detection. The paper also presents bounds on the trace distance between two Gaussian states in terms of the norm distance of their covariance matrices and first moments, providing new technical tools of independent interest. Additionally, the authors analyze the robustness of Gaussian states by examining $t$-doped Gaussian states, which are states prepared by Gaussian unitaries and at most $t$ local non-Gaussian evolutions. They show that these states can be efficiently learned for bounded $t$, demonstrating the efficiency of tomography even in the presence of small perturbations. The paper concludes by highlighting the bridge between quantum learning theory and continuous variable quantum information, providing rigorous performance guarantees for tomography of CV systems and establishing the efficiency of learning Gaussian states and $t$-doped Gaussian states.This paper investigates the task of quantum state tomography, which involves reconstructing a quantum state from measurement data. The authors focus on continuous variable (CV) systems, which are characterized by infinite-dimensional Hilbert spaces, and explore the efficiency of tomography algorithms in these systems. They find that the minimum number of copies required for achieving an $\varepsilon$-approximation in trace distance scales as $\sim \varepsilon^{-2n}$, where $n$ is the number of modes, which is significantly more inefficient compared to finite-dimensional systems. Specifically, for energy-constrained pure states, the optimal sample complexity is established, revealing the extreme inefficiency of CV quantum state tomography. To address this inefficiency, the authors investigate more structured classes of quantum states that can be efficiently tomographed. They prove that Gaussian states, a class of states with physically interesting properties, can be efficiently learned using experimentally feasible measurements such as homodyne and heterodyne detection. The paper also presents bounds on the trace distance between two Gaussian states in terms of the norm distance of their covariance matrices and first moments, providing new technical tools of independent interest. Additionally, the authors analyze the robustness of Gaussian states by examining $t$-doped Gaussian states, which are states prepared by Gaussian unitaries and at most $t$ local non-Gaussian evolutions. They show that these states can be efficiently learned for bounded $t$, demonstrating the efficiency of tomography even in the presence of small perturbations. The paper concludes by highlighting the bridge between quantum learning theory and continuous variable quantum information, providing rigorous performance guarantees for tomography of CV systems and establishing the efficiency of learning Gaussian states and $t$-doped Gaussian states.