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Some background:

The quantum teleportation protocol requires first that Alice and Bob share an entangled state, say a Bell state $|\psi^{+}\rangle_{AB}$. There is another state $|\psi\rangle_{A'}$ to which Bob is to receive. The protocol begins with $|\psi\rangle _{A'} \otimes |\psi^{+}\rangle_{AB}$.

Now, suppose instead of the Bell state I am provided the spatially distributed state as the Werner state is $\rho_{V} = V|\beta(1,1)\rangle\langle\beta(1,1)| + \frac{1-V}{4}$. Clearly, it is a matrix.

My first, and only in fact, approach is to determine the state vector of this Werner state so that I may proceed to understand the effect of replacing a Bell state with a Werner state.

I've been trying to find its state vector but I am unsure how to do so and how to do it efficiently. Any help is appreciated.

glS
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Physkid
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    It's a mixed state with rank greater than 1. It doesn't have a state vector. Instead, you need to learn how to work through the effects of a quantum circuit when applied to a mixed state ($\rho\mapsto U\rho U^\dagger$). – DaftWullie Nov 02 '23 at 11:12
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    you can work out explicitly how teleportation works for a generic mixed state, see eg https://quantumcomputing.stackexchange.com/a/29010/55 – glS Nov 02 '23 at 11:23

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