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arXiv · 2404.15179

Exploring Imaginary Coordinates: Disparity in the Shape of Quantum State Space in Even and Odd Dimensions

Simon Morelli·Santiago Llorens·Jens Siewert
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Abstract

The state of a finite-dimensional quantum system is described by a density matrix that can be decomposed into a real diagonal, a real off-diagonal and and an imaginary off-diagonal part. The latter plays a peculiar role. While it is intuitively clear that some of the imaginary coordinates cannot have the same extension as their real counterparts the precise relation is not obvious. We give a complete characterization of the constraints in terms of tight inequalities for real and imaginary Bloch-type coordinates. Our description entails a three-dimensional Bloch ball-type model for the state space. We uncover a surprising qualitative difference for the state-space boundaries in even and odd dimensions.

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Simon Morelli, Santiago Llorens, Jens Siewert. 2024-04-23. Exploring Imaginary Coordinates: Disparity in the Shape of Quantum State Space in Even and Odd Dimensions. https://doi.org/10.22331/q-2026-07-08-2153

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