Understand the Outer Product of two qubits

[safes007]

Homework Statement

Understanding |1>_a<1|

Relevant Equations

|1>_a<1|

Hi, I'm trying to understand an outer product |1>_a<1| where |1>_a is the ket for one qubit (a) and <1| is the bra for another qubit. Does this make sense and is it possible to express it in terms of tensor products or pauli matrices?

 

[PeroK]

I'm not sure about qubits specifically but in general the outer product of bra and a ket is an operator. E.g

$|\alpha \rangle \langle \beta |$

Is an operator that maps a ket $|\gamma \rangle$ to the ket $|\alpha \rangle \langle \beta | \gamma \rangle$.

In that sense, you can express the operator in terms of Pauli matrices, as you can for any operator.