5

To talk about entanglement, you have to first identify subsystems. In your $d=4$ example, you defined an isomorphism $\mathbb{C}^4\simeq \mathbb{C}^2\otimes\mathbb{C}^2$ via the identification of basis states. Whether this is meaningful, depends on the context/the physical scenario you have in mind. But it definitely can be. For $d=3$, this is never possible....


2

I think the terminology makes sense if you think the matrix $ \Psi $, via the linear bijection $ vec\big( |b \rangle \langle a|\big) = |b \rangle |a \rangle$, as a pure bipartite state $ vec(\Psi) = |\psi \rangle_{AB} = \frac{1}{\sqrt{l}} \sum_{i=1}^{l} | \psi_i \rangle_A | i \rangle_B $ and observe that the reduced density matrix is $$ \rho_B = \text{Tr}_A[\...


1

Is there a clear boundary between quantum coupling and quantum entanglement? If two qubits (or more) are coupled, they can influence each other. This means that they are entangled. If two quantum systems are coupled, do they need to be restricted to a certain distance? Generally not, but increasing the distance increases probability that the system is ...


1

I think this is the quantum circuit that you want, first produce two pairs of Bell states, then undo the second pair coherently, and finally apply two CNOT two flip the last two qubits.


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