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Quantum Potato Chips
Nikolay Murzin, Bruno Tenorio, Sebastian Rodriguez, John McNally, Mohammad Bahrami
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We examine qubit states under symmetric informationally-complete measurements, representing state vectors as probability 4-vectors within a 3-simplex in bb(R)⁴. Using geometric transformations, this 3-simplex is mapped to a tetrahedron in bb(R)³. A specific surface within this tetrahedron allows for the separation of probability vectors into two disjoint 1-simplices. The intersection of this surface with the insphere identifies a "quantum potato chip" region, where probability 4-vectors reduce to two binary classical variables. States within this region can be fully reconstructed using only two given projective measurements, a feature not found elsewhere in the state space.
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