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What's an unknown POVM, and what does a two qubit state look like?

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If probabilities represent knowledge, what is an "unknown

probability"? De Finetti's theorem licenses the view that it is simply a

convenient metaphor for a certain class of knowledge about a series of

events. There are quantum versions for "unknown states" and

channels". I will explain how "unknown measurements" can be


I will then move to a totally different topic. The Bloch sphere is handy

for representing qubit states, but the equivalent for two qubits is

15-dimensional! I will advocate instead drawing the set of states that Bob

can steer Alice to, the "steering ellipsoid". I will show how

and discord look from this perspective, and outline a geometric

classification of separable two qubit states.