Dimensionality and value of $mathbb{I}_A$ in Quantum operations
Quantum Computing Asked on March 8, 2021
I was checking this question answer but I still can’t get what is the value and dimension of $mathbb{I}_A$ in this question and on the answer. Is it an identity matrix or some vector?
It also appears in the answer as $mathbb{I}$ multiple times.
One Answer
It is the identity operator on system $A$ so it has the same size as $rho_A$. To convince yourself further of the solution it may be a good idea to do the calculation yourself with some small matrices. What may be confusing you is that whilst $I_A$ will be a square matrix, $I_A otimes |0rangle$ will not be. However, it will still have the correct dimensions in order to make the product $(I_A otimes |0rangle) rho_A$ well defined.
Correct answer by Rammus on March 8, 2021
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