Question

Q. The total state of a quantum system consisting of two spin 1/2 particles it is given as: $\vert \Psi \rangle = \frac{1}{\sqrt{2}} (\vert \uparrow \rangle_A \otimes \vert \uparrow \rangle_B + \vert \downarrow \rangle_A \otimes \vert \downarrow \rangle_B)$ a) Show that the state of this system, to be called subsystems A and B, cannot be written as a tensor product of the states of these two subsystems that make up the system. $(\vert \Psi \rangle = \vert \psi \rangle_A \otimes \vert \phi \rangle_B)$ to be the most general $|\psi\rangle$ and $|\phi\rangle$ complex numbers and write this equation in the set of statuses that you can show would not have found a solution). b) what is the importance of this type of quantum states for quantum technologies?

          Q. The total state of a quantum system consisting of two spin 1/2 particles it is given as:
$\vert \Psi \rangle = \frac{1}{\sqrt{2}} (\vert \uparrow \rangle_A \otimes \vert \uparrow \rangle_B + \vert \downarrow \rangle_A \otimes \vert \downarrow \rangle_B)$
a) Show that the state of this system, to be called subsystems A and B, cannot be written as a tensor product of the states of these two subsystems that make up the system. $(\vert \Psi \rangle = \vert \psi \rangle_A \otimes \vert \phi \rangle_B)$ to be the most general $|\psi\rangle$ and $|\phi\rangle$ complex numbers and write this equation in the set of statuses that you can show would not have found a solution).
b) what is the importance of this type of quantum states for quantum technologies?

Q. The total state of a quantum system consisting of two spin 1/2 particles it is given as:
|Ψ⟩ = (1)/(√(2)) (|↑⊗|↑ + |↓⊗|↓)
a) Show that the state of this system, to be called subsystems A and B, cannot be written as a tensor product of the states of these two subsystems that make up the system. (|Ψ⟩ = |ψ⊗|ϕ) to be the most general |ψ⟩ and |ϕ⟩ complex numbers and write this equation in the set of statuses that you can show would not have found a solution).
b) what is the importance of this type of quantum states for quantum technologies?

Added by Albert G.

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