Reduced Density Matrix - Example

In this video, we go over an example of how to use the definition of the partial trace to derive the reduced density matrix in a composite system. CORRECTION: Around minute 8:50, we perform the inner product of the term |0_B⟩⟨0_A 0_B| (in red) with the term |0_A 0_B⟩⟨0_A 0_B| of ρ_AB (in white) and obtain 1/2 |0_B⟩⟨0_A 0_B|. Here, we forgot to also perform the inner product with the term |0_A 0_B⟩⟨1_A 1_B| of ρ_AB (also in white), so in min 9:15 there isn't just only "one term that survives", but two. The full expression at that point in the video should be: 1/2[ |0_B⟩⟨0_A 0_B| + |0_B⟩⟨1_A 1_B| ] That being said, this second term |0_B⟩⟨1_A 1_B| does cancel out in the text step when we perform inner products with the terms on the right (in green) because there is no |1_A 1_B⟩ in that part of expression, so the final result is indeed correct. This is part of the following series of videos on the Density Matrix and Mixed States: playlist: https://youtube.com/playlist?list=PLhI5X1mNN8ghnH1ckAcclxY6-CPmZvWrk For new video updates, please subscribe, or follow me on twitter https://twitter.com/diemilioser