{"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 cat state 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 parameters \u03c6 and \u03b1, and the relative entropy measure compares the non-Gaussian state to a reference Gaussian state. The goal is to compute the non-Gaussianity for specific values of \u03c6 and \u03b1, leading to the expected result of 1.38. This involves evaluating the density matrices and applying the relative entropy formula."}