{"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 given parameters (phi = -pi/4 and alpha = 0.5) and using the provided formulas for the state and the relative entropy measure.", "goal": "Determine the amount of non-Gaussianity (nG) in the specified Schr\u00f6dinger cat state."}, "summary": "To calculate the non-Gaussianity (nG) of the Schr\u00f6dinger cat state defined by the given parameters, we need to evaluate the relative entropy measure between the non-Gaussian state and a reference Gaussian state. The state is parameterized by phi and alpha, and the normalization constant N is derived from these parameters. By substituting phi = -pi/4 and alpha = 0.5 into the formulas for the density matrices and the relative entropy, we can compute the nG value. The candidates for the nG value are provided, and the calculation will lead us to the correct answer."}