user1936752

I'd call this quite fussy and difficult behavior if my employee did this. It sounds like something you should be able to figure out on your own.

@Neuromancer I know - it's just one of those moments when HR cements their reputation for being a useless element of our working culture.

It seems HR has nothing else to do and is trying to find "work" for themselves.

Meant to say that in my first comment I wrongly wrote J(rho) = 1 for max mixed state, when in fact, it is zero which I corrected myself to in my second comment.

@gIS

This is what is being referred to as the maximally mixed state.

I have no objection to your answer and I even upvoted it. I initially thought J(\rho) was zero for maximally mixed state and then corrected myself in my comment because my very first comment was wrong. Also, I suspect there is one thing that you might be misunderstanding which is that the identity matrix in $H_A\otimes H_B$ is always the product of individual identities. $diag(1,1,..)$ on a joint space is always $diag(1,1,..)\otimes diag(1,1...)$

@gIs

If you still think a max mixed state can generate correlations, please provide a reference.

A maximally mixed state can always be written as a product state. $I_{AB} = I_A\otimes I_B$. The statement that you can observe correlations if two parties share a maximally mixed state is simply not true

I gotta go now, but we can chat later if it's still not clear

For the maximally mixed state, I'm pretty sure you have any correlations. (You can replace 1 in my argument with log(d), that's just me being lazy). But the first point is important - measuring something in B does not do anything to A if the global state is maximally mixed.

According to the defintion of $J$, what you do is take a bipartite state. So here we have $I_{AB} = I_A\otimes I_B$. $S(\rho_A) = 1$ since the reduced state is also maximally mixed. According to the defintion, what you do next is measure system $B$ in the computational basis assuming the outcome is $i$, check $S(\rho_A^i)$. This is still maximally mixed since measuring in $B$ can't change the $A$ part. So for the maximally mixed state, $J(\rho) = 0$. If Alice and Bob hold a maximally mixed state, Bob can do whatever he wants with his state and there can be no effect on Alice's side.

Sorry, I was wrong. $J(\rho) = 0$ for max mixed state (the POVM is on B!). And this is correct since there are no correlations of any kind in the maximally mixed state.

I would add that it's a bit weird though that $J(\rho) = 1$ for both the maximally mixed state and the maximally entangled state. Surely, a measure of correlations ought to give you 0, at least for the maximally mixed state?

Makes me question if I even understand the basic formalism of pure states and mixed states...

Sorry, I'm using the chat for the first time so I'm not sure if this is the right place but does anyone have thoughts on Sandu Popescu's recent note on the arxiv? arxiv.org/abs/1811.05472