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Convexity and Is the set of all states with negative conditional vonVon Neumann Entropyentropy convex?

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Convexity and Conditionalconditional von Neumann Entropy

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Convexity and Conditional Vonvon Neumann Entropy

I have read somewhere  / heard that the set of all states that have non-negative conditional Von Neumann entropy forms a convex set. Is this true? Is there a proof for it?

Can anything be said about the reverse - set of all states that have negative conditional Von Neumann entropy?

Convexity and Conditional Von Neumann Entropy

I have read somewhere/ heard that the set of all states that have non-negative conditional Von Neumann entropy forms a convex set. Is this true? Is there a proof for it?

Can anything be said about the reverse - set of all states that have negative conditional Von Neumann entropy?

Convexity and Conditional von Neumann Entropy

I have read somewhere  / heard that the set of all states that have non-negative conditional Von Neumann entropy forms a convex set. Is this true? Is there a proof for it?

Can anything be said about the reverse - set of all states that have negative conditional Von Neumann entropy?

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