What does the unitary $[|0\rangle\langle 0|\otimes I+|1\rangle\langle1|\otimes(|1\rangle\langle 0|+|0\rangle\langle1|)]\otimes I$ represent?

Question

Consider the following unitary defined for a system $A$ interacting with a bipartite system $BB^\prime$

$$U_{AB} = \Big[|0\rangle \langle 0|_{A} \otimes \mathbf{I}_{B} + |1\rangle \langle 1|_{A} \otimes \big(|1\rangle \langle 0|_{B} + |0\rangle \langle 1|_{B} \big) \Big] \otimes \mathbf{I}_{B^\prime},$$ with $\mathbf{I}_i$ being the identity.

My question:

1. What is the physical meaning of operation $U_{AB}$?

2. Can one represent $U_{AB}$ in terms of quantum logic gates ( a circuit diagram)?

Answer 1

The gate/operator in the brackets is the non-local CNOT gate, frequently used to create bipartite entanglement. Given it itself is a 2 qubit gate, then the tensor of this with the identity is simply a gate that acts on 3 qubits.

This gate will take a 3 qubit state and flip the second qubit of this state when the first is $|1\rangle$ It will take $|110\rangle \to|100\rangle, |111\rangle \to |101\rangle$ and vice-versa.

Edit: important to note is that $|1\rangle\langle 0|+|0\rangle\langle 1|$ is the Pauli X gate