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

• URL: http://arxiv.org/abs/2404.15179v1
• Date: Tue, 23 Apr 2024 16:19:38 GMT
• Title: Exploring Imaginary Coordinates: Disparity in the Shape of Quantum State Space in Even and Odd Dimensions
• Authors: Simon Morelli, Santiago Llorens, Jens Siewert,
• Abstract summary: We give a complete characterization of the constraints in terms of tight inequalities for real and imaginary Bloch-type coordinates. We uncover a surprising qualitative difference for the state-space boundaries in even and odd dimensions.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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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