The geometry of state space

M. Adelman; J. V. Corbett; C. A. Hurst

doi:10.1007/BF01883625

The geometry of state space

M. Adelman^*, J. V. Corbett, C. A. Hurst

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

26 Citations (Scopus)

Abstract

The geometry of the state space of a finite-dimensional quantum mechanical system, with particular reference to four dimensions, is studied. Many novel features, not evident in the two-dimensional space of a single spin, are found. Although the state space is a convex set, it is not a ball, and its boundary contains mixed states in addition to the pure states, which form a low-dimensional submanifold. The appropriate language to describe the role of the observer is that of flag manifolds.

Original language	English
Pages (from-to)	211-223
Number of pages	13
Journal	Foundations of Physics
Volume	23
Issue number	2
DOIs	https://doi.org/10.1007/BF01883625
Publication status	Published - Feb 1993

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abstract = "The geometry of the state space of a finite-dimensional quantum mechanical system, with particular reference to four dimensions, is studied. Many novel features, not evident in the two-dimensional space of a single spin, are found. Although the state space is a convex set, it is not a ball, and its boundary contains mixed states in addition to the pure states, which form a low-dimensional submanifold. The appropriate language to describe the role of the observer is that of flag manifolds.",

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AB - The geometry of the state space of a finite-dimensional quantum mechanical system, with particular reference to four dimensions, is studied. Many novel features, not evident in the two-dimensional space of a single spin, are found. Although the state space is a convex set, it is not a ball, and its boundary contains mixed states in addition to the pure states, which form a low-dimensional submanifold. The appropriate language to describe the role of the observer is that of flag manifolds.

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The geometry of state space

Abstract

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