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### Semi-definite program for smooth min-entropy

You do not need a double objective function to solve this. Given $\rho_{AB}$ let $\rho_{ABC}$ be any purification of $\rho_{AB}$. Then we can write the smooth min-entropy as the following SDP \begin{...
• 5,853
Accepted

### Semi-definite program for conditional smooth max-entropy

Yes, you can formulate the smooth max-entropy as an SDP. The author of the book you linked notes this when they explain how to derive the SDP for the smooth min-entropy that you reference on page 91. ...
• 5,853
Accepted

### Are all extremal points of the feasible set of an arbitrary affine equation pure states?

A simple counterexample but perhaps I'm misinterpreting "one affine equation". Take the map $\Lambda$ to be the identity map and let $Y$ be any mixed state. Then the set of states satisfying ...
• 5,853

### How to calculate the conditional min-entropy via a semidefinite program?

I think I have an answer. The following should be the CVX code for one of the formulations found in this link. ...
• 1,785
1 vote

### Are all extremal points of the feasible set of an arbitrary affine equation pure states?

This is generally not the case. One example is the set of CPTP maps. Under the Choi-Jamiołkowski isomorphism, this set corresponds to a set of quantum states intersected with an affine hyperplane ...
• 5,047
1 vote

### $3 \rightarrow 1$ QRAC encoding for XOR functions

I found a way to do it for the $2\to1$ QRAC. I simply guessed that we could leave the measurement bases as they are, $Z$ for the first bit, and $X$ for the second bit, and added $Y$ as the basis with ...
• 2,551

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