{"knowledge_schema": {"broad_category": "Quantum Mechanics \u2192 Quantum States \u2192 Non-Gaussianity", "refinement": "This problem involves calculating the non-Gaussianity of a specific quantum state known as a Schr\u00f6dinger cat state using the relative entropy measure.", "specific_scope": "The focus is on evaluating the non-Gaussianity for a given set of parameters (phi = -pi/4 and alpha = 0.5) and comparing it to a reference Gaussian state.", "goal": "Calculate the relative entropy measure to quantify the non-Gaussianity of the specified Schr\u00f6dinger cat state."}, "summary": "The problem requires calculating the non-Gaussianity of a Schr\u00f6dinger cat state using the relative entropy measure. The state is defined with parameters phi and alpha, and the normalization constant is provided. The relative entropy is computed by comparing the density matrix of the non-Gaussian state with that of a reference Gaussian state. For the given parameters (phi = -pi/4 and alpha = 0.5), the calculated non-Gaussianity is found to be 1.38."}