{"knowledge_schema": {"broad_category": "Quantum Mechanics \u2192 Quantum States \u2192 Non-Gaussianity", "refinement": "This problem involves calculating the level of non-Gaussianity in a specific quantum state known as a Schr\u00f6dinger cat state using the relative entropy method.", "specific_scope": "The focus is on evaluating the relative entropy between a non-Gaussian state represented by a superposition of coherent states and a reference Gaussian state, specifically for given parameters \u03c6 and \u03b1.", "goal": "Calculate the non-Gaussianity (nG) of the Schr\u00f6dinger cat state for \u03c6 = -\u03c0/4 and \u03b1 = 0.5, using the relative entropy measure to arrive at the expected result of 1.38."}, "summary": "This problem requires calculating the level of non-Gaussianity in a Schr\u00f6dinger cat state using the relative entropy method. The state is defined by a superposition of coherent states, and the calculation involves determining the relative entropy between the non-Gaussian state and a reference Gaussian state. By substituting the given parameters \u03c6 = -\u03c0/4 and \u03b1 = 0.5 into the equations, the expected result of 1.38 can be achieved, confirming the non-Gaussianity of the state."}