Quantum Potato Chips

Research Paper
Written By Nikolay Murzin

Authors:

  • Nikolay Murzin

  • Bruno Tenorio

  • Sebastian Rodriguez

  • John McNally

  • Mohammad Bahrami

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.

Permalink:

https://doi.org/10.48550/arXiv.2504.16225

Nikolay Murzin
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