Discussion Overview
The discussion revolves around calculating the matrix representation of the outer product |11><11| for two qubits. Participants explore the correct formulation of the matrix and the implications of basis vector ordering in this context.
Discussion Character
- Technical explanation
- Conceptual clarification
- Debate/contested
Main Points Raised
- One participant states that forming the matrix representation of |1><1| is straightforward, but they seek help with |11><11|, providing an initial incorrect matrix.
- Another participant suggests that |1> can be represented as (1 0)t, leading to the conclusion that |11> is (1 0 0 0)t, resulting in a matrix with a 1 in the upper left corner and zeros elsewhere.
- A clarification is provided by a participant who interprets |11> as (0 1 0 1) and <10 as (0 1 1 0), expressing confusion over the outer product having more than one non-zero entry.
- Another participant proposes that |11< refers to (0 0 0 1) and <10 refers to (0 1 0 0), questioning if this is correct.
- A later reply emphasizes that the matrix elements depend on the order of the basis vectors, suggesting a specific ordering and providing the resulting matrix for |11><11| as a projection operator in a 4-dimensional space.
- A participant acknowledges that their issue stemmed from incorrectly ordering the basis vectors, expressing a lingering concern about the necessity of such ordering in relation to nature.
Areas of Agreement / Disagreement
Participants express differing interpretations of the matrix representation and the ordering of basis vectors, indicating that multiple competing views remain and the discussion is unresolved.
Contextual Notes
Participants highlight the dependence of matrix representation on the chosen order of basis vectors, which remains a point of contention and uncertainty.