By using Quantum Neural Networks (QNNs), the principles of quantum computing can be employed to perform supervised learning on quantum computers. Herein, a unitary transformation is trained using sets of quantum input states and their associated outputs. When the exact output states of the transformation are known, recent results show that entanglement can drastically reduce the approximation error of a QNN, without increasing the number of required training samples. However, the exact output states might not be readily available. In certain scenarios, only the measurement outcomes of these quantum states after measurement with an observable are available. Therefore, this work investigates the effect of entangled training samples when training using measurement outcomes. For observables described by one-dimensional projectors, we specify entangled training samples that minimize the approximation error. Furthermore, we validate our findings on a simulator and show that when using entangled training samples, the approximation error depends on the factorization of the entangled samples.