Quantum Potato Chips

• URL: http://arxiv.org/abs/2411.01082v1
• Date: Fri, 01 Nov 2024 23:38:37 GMT
• Title: Quantum Potato Chips
• Authors: Nikolay Murzin, Bruno Tenorio, Sebastian Rodriguez, John McNally, Mohammad Bahrami,
• Abstract summary: We examine qubit states under symmetric informationally-complete measurements. Using geometric transformations, a 3-simplex is mapped to a tetrahedron in $bb(R)3$. The intersection of this surface with the insphere identifies a "quantum potato chip" region.
• Score: 1.7825757481227436
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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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