Information geometry of density matrices and state estimation
Open accessAbstract
Given a pure state vector | x ⟩ and a density matrix , the function defines a probability density on the space of pure states parameterised by density matrices. The associated Fisher–Rao information measure is used to define a unitary invariant Riemannian metric on the space of density matrices. An alternative derivation of the metric, based on square-root density matrices and trace norms, is provided. This is applied to the problem of quantum-state estimation. In the simplest case of unitary parameter estimation, new higher-order corrections to the uncertainty relations, applicable to general mixed states, are derived.
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The analytical formulas of the fidelity F(ρ0,ρτ) and the affinity A(ρ0,ρτ) for any pair of one-qubit states are given by Eqs. (A12) and (A13).
“where the analytical formulas of the fidelity Fðρ 0 ; ρ τ Þ and the affinity Aðρ 0 ; ρ τ Þ for any pair of one-qubit states ρ 0 and ρ τ are the following [29,73,74]:”
From Generalized Geometric Quantum Speed Limits (2016) · cites this paper as [74]
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Cites
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Geodesic Execution Slippage: A Statistical Physics Framework for Cryptocurrency Liquidity Risk
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- Authors
- Brody, D. C.
- Affiliations
- Brunel University of London (GB)
- Corresponding author
- Brody, Dorje C
- ORCID
- Brody, Dorje C
- Venue
- Journal of Physics A: Mathematical and Theoretical
- Publisher
- IOP Publishing
- Published
- 2011-05-19
- Volume
- 44
- Issue
- 25
- Pages
- 252002
- ISSN
- 1751-8113 (ISSN-L)
- 1751-8121
- OpenAlex
- W2045278314
- Cited by
- 32
- References
- 19
- Citations by year
- 2026: 1 · 2023: 2 · 2022: 1 · 2021: 3 · 2020: 3 · 2019: 3 · 2018: 2 · 2017: 2 · 2016: 3 · 2015: 5 · 2014: 2 · 2013: 3 · 2012: 2
- FWCI
- 1.22
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Journal of Physics A Mathematical and Theoretical (publishedVersion)
- arXiv (Cornell University) (publishedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Keywords
- information geometry, density matrix, Fisher information metric, Riemannian metrics, unitary invariance, trace norm, quantum state estimation, uncertainty relations, mixed states, pure states
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