2024/05/27 by Christopher Langrenez, Wilfred Salmon, Langrenez, Christopher +10 · 1 voice · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Advanced Operator Algebra Research #Homotopy and Cohomology in Algebraic Topology #Quantum Information and Cryptography #Quantum Mechanics and Applications #Statistical Mechanics and Entropy
paper · doi:10.1103/v7z4-qsz8
openalex publication_date 2026/04/07 · openalex created_date 2026/04/08 · openalex updated_date 2026/06/17
A central problem in quantum information is determining quantum-classical boundaries. In the quasiprobability framework, a state is called classical if it is represented by a quasiprobability distribution that is positive, and thus a probability distribution. In recent years, the Kirkwood-Dirac (KD) distributions have gained much interest due to their numerous applications in modern quantum-information research. A particular advantage of the KD distributions is that they can be defined with respect to arbitrary observables. Here, we show that if two d-dimensional observables are picked at random, the set of classical (positive) states of the resulting KD distribution is a minimal polytope of dimension 2(d-1) with 2d explicitly known vertices. This implies minimality of the sets of KD-real observables, of KD-positive measurement elements and of KD-positivity-preserving unitaries. We show how these results have implications on robust observations of nonclassical phenomena, on classical simulations of quantum circuits, and on foundations of quantum theory.