Higher dimensional bipartite composite systems with the same density matrix: separable, free entangled, or PPT entangled?

Finite projective geometries, especially the Fano plane, have been observed to arise in the context of certain quantum gate operators. We use Clifford algebras to explain why these geometries, both planar and higher dimensional, appear in the context of multi-qubit composite systems.

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Damage mechanism identification in composites via machine learning and acoustic emission

npj Computational Materials ◽

10.1038/s41524-021-00565-x ◽

2021 ◽

Vol 7 (1) ◽

Author(s):

C. Muir ◽

B. Swaminathan ◽

A. S. Almansour ◽

K. Sevener ◽

C. Smith ◽

...

Keyword(s):

Machine Learning ◽

Acoustic Emission ◽

Damage Mechanism ◽

Comprehensive Understanding ◽

Monitoring Design ◽

Learning Framework ◽

Composite Systems ◽

Higher Dimensional ◽

Analysis Strategies ◽

Waveform Feature

AbstractDamage mechanism identification has scientific and practical ramifications for the structural health monitoring, design, and application of composite systems. Recent advances in machine learning uncover pathways to identify the waveform-damage mechanism relationship in higher-dimensional spaces for a comprehensive understanding of damage evolution. This review evaluates the state of the field, beginning with a physics-based understanding of acoustic emission waveform feature extraction, followed by a detailed overview of waveform clustering, labeling, and error analysis strategies. Fundamental requirements for damage mechanism identification in any machine learning framework, including those currently in use, under development, and yet to be explored, are discussed.

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Classical analogue of the statistical operator

Open Physics ◽

10.2478/s11534-014-0438-y ◽

2014 ◽

Vol 12 (3) ◽

Author(s):

Angelo Plastino ◽

Angel Plastino ◽

Claudia Zander

Keyword(s):

Density Matrix ◽

Quantum Mechanical ◽

Marginal Probability ◽

Marginal Density ◽

Partial Trace ◽

Statistical Correlations ◽

Composite Systems ◽

Probability Densities ◽

Classical Analogue ◽

Statistical Operator

AbstractWe advance the notion of a classical density matrix, as a classical analogue of the quantum mechanical statistical operator, and investigate its main properties. In the case of composite systems a partial trace-like operation performed upon the global classical density matrix leads to a marginal density matrix describing a subsystem. In the case of dynamically independent subsystems (that is, non-interacting subsystems) this marginal density matrix evolves locally, its behavior being completely determined by the local phase-space flow associated with the subsystem under consideration. However, and in contrast with the case of ordinary marginal probability densities, the marginal classical density matrix contains information concerning the statistical correlations between a subsystem and the rest of the system.

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