Postulate 4: composition Composition: The state of the joint system (S1, S2, where S, is in state l 1 and s2 in y2),is|y1)②|v2) tensor product of vectors (a1,a2)⑧(b1,b2b3)=(a1b1,a1b2,a1b3,a2b1,a2b2a2b3) dim( 1&1 2))=dim( 1)). dimdya2)) size (l idly b2))=size (ly1))+ size(l b2)) size: number of qubits Notation:|0)8n=|0)⑧…|0), m timesPostulate 4: composition • Composition: The state of the joint system (𝑆1, 𝑆2), where 𝑆1 is in state 𝜓1 and 𝑆2 in 𝜓2 , is 𝜓1 ⊗ 𝜓2 . • ⊗: tensor product of vectors. – 𝑎1, 𝑎2 ⊗ 𝑏1, 𝑏2, 𝑏3 = (𝑎1𝑏1, 𝑎1𝑏2, 𝑎1𝑏3, 𝑎2𝑏1, 𝑎2𝑏2, 𝑎2𝑏3). – dim 𝜓1 ⊗ 𝜓2 = dim 𝜓1 ⋅ dim 𝜓2 – size 𝜓1 ⊗ 𝜓2 = size 𝜓1 + size 𝜓2 • size: number of qubits. • Notation: 0 ⊗𝑛 = 0 ⊗ ⋯ ⊗ 0 , 𝑛 times