# Tag Info

Accepted

### What is a separable decomposition for the Werner state?

The way that I think about this is to take a decomposition in Paulis, $$\rho_z=(I+zZ\otimes Z-zX\otimes X-zY\otimes Y)/4.$$ I can group these as  ((1-3z)I+z(I+Z\otimes Z)+z(I-X\otimes X)+z(I-Y\...
• 59.5k
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### For 2x2 and 2x3 systems, is the partial transpose the only positive but not CP operation?

The partial transpose is not the only positive but not completely positive operation that is possible on 2x2 and 2x3 systems. Trivially, any completely positive operation (such as a local unitary) ...
• 59.5k
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### Why is $\rho$ NPT if and only if $\rho^{\otimes N}$ is NPT?

The short answer is that $(\rho^{\otimes N})^{T_B}=(\rho^{T_B})^{\otimes N}$. More explicitly, if $\rho=\sum_{ii'jj'}\rho_{ii',jj'}|i\rangle\!\langle i'|\otimes |j\rangle\!\langle j'|$, then we can ...
• 25.6k
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### How are witness operators physically implemented?

This is certainly how theorists think of this being done. I don't know if there's an experimental reality to compare this to. Whether they actually decompose it in terms of the eigenvectors, or find ...
• 59.5k
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### Are there unextendable product sets in $\mathbb{C}^2\otimes\mathbb{C}^2$?

Upon some reflection I realised that, no, there can't be any such set in $\mathbb{C}^2\otimes\mathbb{C}^2$ or $\mathbb{C}^2\otimes\mathbb{C}^3$. That's because, as discussed shortly thereafter in the ...
• 25.6k
### What are the ranges of the four $q$ parameters in the magic simplex of Bell states formula?
It looks like the only relation they say is $\text{IdentityMatrix}[3^2]=\sum P_{k,l}$. You get a linear combination of $P_{k,l}$. Those are vertices of a $d^2-1$ simplex so the coefficents $c_{k,l}$ ...