They are being 2 by 2 matrices and I being the identity. Physically they are Pauli matrices.(adsbygoogle = window.adsbygoogle || []).push({});

1. Is $$((A\otimes I\otimes I) + (I\otimes A\otimes I) + (I\otimes I\otimes A))\otimes B$$

= $$(A\otimes I\otimes I)\otimes B + (I\otimes A\otimes I)\otimes B + (I\otimes I\otimes A)\otimes B$$? I think so.

2. Is $$(A\otimes I\otimes I)\otimes B + (I\otimes A\otimes I)\otimes B + (I\otimes I\otimes A)\otimes B$$=

$$(A\otimes B)\otimes (I\otimes I)\otimes (I\otimes I) + (I\otimes I)\otimes (A\otimes B)\otimes (I\otimes I) + (I\otimes I)\otimes(I\otimes I)\otimes(A\otimes B)$$? I am not sure.

Note that they are no scalar product here. I ask 2 because I stumbled upon the RHS of 2 and hope to know if it can be factored out as the LHS of 1. So basically I reverse the line of reason to ask these two questions. Looking at the LHS of 1., I also want to know:

3. Is $$((A\otimes I\otimes I) + (I\otimes A\otimes I) + (I\otimes I\otimes A))\otimes B$$

= $$((A\otimes I\otimes I) + (I\otimes A\otimes I) + (I\otimes I\otimes A))\otimes (B\otimes I\otimes I)$$

= $$((A\otimes I\otimes I) + (I\otimes A\otimes I) + (I\otimes I\otimes A))\otimes (I\otimes B\otimes I)$$

=$$((A\otimes I\otimes I) + (I\otimes A\otimes I) + (I\otimes I\otimes A))\otimes (I\otimes I\otimes B)$$? I do not think so as I do not think I can enlarge the dimension of B here?

This is not homework.

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# A Question about properites of tensor product

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