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I want to represent Werner state in the form of ket vector notation. Is there a way in which I can represent it in vector form?

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  • $\begingroup$ in what form have you seen it written? $\endgroup$
    – glS
    Jun 6, 2021 at 9:28
  • $\begingroup$ I saw it in density matrix form. $\endgroup$
    – Ganesh M
    Jun 7, 2021 at 6:48
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    $\begingroup$ @GaneshM What exactly do you mean by vector form. They are mixed states for all but one point in their family and so you need density matrices to describe them. $\endgroup$
    – Rammus
    Jun 7, 2021 at 7:35

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From quantiki we have $$\rho=p_{\mathrm{sym}}\frac{2\hat{P}_{\mathrm{sim}}}{d^2+d}+(1-p_{\mathrm{sym}})\frac{2\hat{P}_{\mathrm{anti-sym}}}{d^2-d}, $$ where $p_{\mathrm{sym}}$ is the probability of being in the symmetric subspace, $d$ is the dimension of the state vectors, the projectors onto the symmetric and anti-symmetric subspaces are given by $$\hat{P}_{\mathrm{sym}}=\frac{1+\hat{P}}{2}$$ and $$\hat{P}_{\mathrm{anti-sym}}=\frac{1-\hat{P}}{2},$$ and, finally, we can connect everything to state vectors through the definition of the exchange operator $$\hat{P}=\sum_{i,j}|i\rangle\langle j|\otimes |j\rangle\langle i|.$$ Here we have used an arbitrary set of basis states for each system.

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