# Bra-ket notation to Matrix for entangled pairs

1. May 5, 2012

I am confused about the the notation |ab> for an entangled pair. Isn't this the same as the tensor product |a> $\otimes$ |b>? If so, I run into another confusion when using the corresponding matrices. I read that I should apply a Hadamard operator H twice to the input state |01>. Does this mean (H|0>)$\otimes$ (H|1>)? I don't see how it could mean H(H(|01>), since |01> is represented by a four-by-one matrix, whereas H is represented by a two-by-two matrix. So what does this mean? Thanks