# How do I represent a Werner state in ket notation?

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?

• in what form have you seen it written?
– glS
Jun 6, 2021 at 9:28
• I saw it in density matrix form. Jun 7, 2021 at 6:48
• @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. Jun 7, 2021 at 7:35

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.