Entropy Distance: New Quantum Phenomena
arXiv:1007.5464 · doi:10.1063/1.4757652
Abstract
We study a curve of Gibbsian families of complex 3x3-matrices and point out new features, absent in commutative finite-dimensional algebras: a discontinuous maximum-entropy inference, a discontinuous entropy distance and non-exposed faces of the mean value set. We analyze these problems from various aspects including convex geometry, topology and information geometry. This research is motivated by a theory of info-max principles, where we contribute by computing first order optimality conditions of the entropy distance.
34 pages, 5 figures
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Cited by in corpus (21)
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- Measures of quantum correlations in infinite-dimensional systems
- General Quantum Resource Theories: Distillation, Formation and Consistent Resource Measures
- Quantum Convex Support
- Discontinuity of Maximum Entropy Inference and Quantum Phase Transitions
- Maximizing the divergence from a hierarchical model of quantum states
- Characterizing ground and thermal states of few-body Hamiltonians
- Continuity of the maximum-entropy inference: Convex geometry and numerical ranges approach
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- Asymptotically Consistent Measures of General Quantum Resources: Discord, Non-Markovianity, and Non-Gaussianity
- Quantum thermodynamics with multiple conserved quantities
- A new signature of quantum phase transitions from the numerical range
- Maximum-entropy inference and inverse continuity of the numerical range
- Pre-images of extreme points of the numerical range, and applications
- A variation principle for ground spaces
- Quantum marginals, faces, and coatoms
- Matrix systems, algebras, and open maps