This paper investigates the efficiency of quantum state tomography for continuous variable (CV) systems, focusing on the sample complexity required to achieve a given trace distance error. The study reveals that learning energy-constrained n-mode states without additional assumptions is extremely inefficient, with the number of state copies needed scaling as $ \sim \varepsilon^{-2n} $, in stark contrast to the $ \sim \varepsilon^{-2} $ scaling for n-qudit systems. This phenomenon, termed 'extreme inefficiency', highlights the fundamental challenges in tomography for CV systems. The paper then explores whether more structured classes of quantum states, such as Gaussian states, can be efficiently tomographed. It rigorously proves that Gaussian states can be efficiently learned, with the trace distance error depending on the precision of estimating the first and second moments of the state. This result is significant as it provides a new technical tool for Gaussian quantum information. The study also examines t-doped Gaussian states, which are prepared by Gaussian unitaries and at most t local non-Gaussian evolutions. It shows that these states can still be efficiently learned, even with small perturbations from Gaussian states. The paper presents a tomography algorithm that leverages Gaussian unitaries and measurements like homodyne and heterodyne detection, which are experimentally feasible. The paper concludes that while CV tomography is highly inefficient for arbitrary states, it is efficient for structured classes like Gaussian states. This work bridges quantum learning theory and continuous variable quantum information, providing rigorous performance guarantees for tomography of CV systems. The results highlight the importance of identifying experimentally relevant classes of states that are easy to learn, which is crucial for the practical implementation of quantum technologies.This paper investigates the efficiency of quantum state tomography for continuous variable (CV) systems, focusing on the sample complexity required to achieve a given trace distance error. The study reveals that learning energy-constrained n-mode states without additional assumptions is extremely inefficient, with the number of state copies needed scaling as $ \sim \varepsilon^{-2n} $, in stark contrast to the $ \sim \varepsilon^{-2} $ scaling for n-qudit systems. This phenomenon, termed 'extreme inefficiency', highlights the fundamental challenges in tomography for CV systems. The paper then explores whether more structured classes of quantum states, such as Gaussian states, can be efficiently tomographed. It rigorously proves that Gaussian states can be efficiently learned, with the trace distance error depending on the precision of estimating the first and second moments of the state. This result is significant as it provides a new technical tool for Gaussian quantum information. The study also examines t-doped Gaussian states, which are prepared by Gaussian unitaries and at most t local non-Gaussian evolutions. It shows that these states can still be efficiently learned, even with small perturbations from Gaussian states. The paper presents a tomography algorithm that leverages Gaussian unitaries and measurements like homodyne and heterodyne detection, which are experimentally feasible. The paper concludes that while CV tomography is highly inefficient for arbitrary states, it is efficient for structured classes like Gaussian states. This work bridges quantum learning theory and continuous variable quantum information, providing rigorous performance guarantees for tomography of CV systems. The results highlight the importance of identifying experimentally relevant classes of states that are easy to learn, which is crucial for the practical implementation of quantum technologies.