In this article, we reflect on dynamical evolution of bipartite correlations in quantum states. An especially strong correlation between particles can result in a single unified quantum state, as initially theorised by Einstein, Rosen, and Podolsky. In this unified state, the measurement of one strongly correlated particle has a direct effect on the other, regardless of the distance between them.

A synergistic mechanism of quantum tunnelling that preserves the information exchange in scale-space has been derived in our work2. We have analysed the evolution dynamics of stochastic resonance synergies for different parameters entanglement, along various dimensions and scales1-8. In our description, a wormhole binds two distinct clusters of quantum particles with various degrees of entanglement.

From astrophysics to quantum biology. The underlying dynamics of quantum tunnelling

We have investigated the cascading events of genotype information processing of coupled oscillators that preserve information by the mass conservation principle. Double spaced clusters exchange information by the scale-space wave information propagation and quantum tunnelling.

This quantum computing approach applies the principle of least action, as described in our reports. The quantum field encodes transition symmetries of synergistically coupled clusters of information in Lagrangian dynamics. The expression of the exploration of configuration space is given by its path integral. At the state of scale resonance, two coupled oscillators encode a quadrupole - the 5D wave descriptor of quantum information. Accordingly, the relationship between holography and quantum gravity derives from the underlying dynamics of the scale-space wave information propagation and quantum tunnelling.

Topological maps of coupled regions have been applied in various topics, mathematically described by the quantum information theory of stochastic resonance synergies.

Genotype information and topology of 5-dimensional scaling

We extend on with the consideration of bipartite correlations to quadrupoles of information carriers, connecting two distinct scale-spaces. In our view, this approach applies to the networked neural systems, as well5-8.

Internal states of a networked neural system are compared by its interaction with the environment via coupled information propagation and coordinate frames transformations. Dynamical cascades map multidimensional information in multiple scales at transition symmetries.

Sampling genotype information in triplets describes our approach to the non-polynomial topological maps. Such a computational problem is pervasive in life sciences, especially. Although this approach results in generally chaotic dynamics, in a deterministic interpretation, the predictability of an outcome of the genotype information expressions is given in probability. We envision this methodology as a core to different applications in life sciences, from bioinformatics to cognitive psychology.

Concluding remarks

"One quadrupole universe" -- in rephrasing John Wheeler. Dynamical cascades map multidimensional information in multiple scales.

We have reflected on the relationship between holography and quantum gravity. A quadrupole carries information of two distinct scale-spaces connected by stochastic resonance synergies. The synergistic mechanism of bipartite correlations preserves information in transition symmetries and evolution of quantum states distributions by 5D coordinate transformations. In this approach, the quantum entanglement and a wormhole represent two attributes of the same wave function.

The underlying dynamics of scale-space wave information propagation and quantum tunnelling have been applied in different networked complex systems1-8.

Notes

1 Jovovic, M., Image segmentation for feature selection from motion and photometric information by clustering, SPIE Symposium on Visual Information Processing V, Orlando, 1996.
2 Jovovic, M., Hierarchical scale quantization and coding of motion information in image sequences, Informacione Tehnologije VI, Zabljak, 2002.
3 Jovovic, M., H. Yahia, and I. Herlin, Hierarchical scale decomposition of images – singular features analysis, INRIA, 2003.
4 Jovovic, M., and G. Fox, Multi-dimensional data scaling – dynamical cascade approach, Indiana University, 2007.
5 Jovovic, M., Stochastic Resonance Synergetics – Quantum Information Theory for Multidimensional Scaling, Journal of Quantum Information Science, 5/2:47-57, 2015.
6 Jovovic, M., A Markov random fields model for describing inhomogeneous textures: generalized random stereograms. IEEE Workshop Proceedings on Visualization and Machine Vision, and IEEE Workshop Proceedings on Biomedical Image Analysis, Seattle, 1994.
7 Jovovic, M., S. Jonic, and D. Popovic, Automatic synthesis of synergies for control of reaching – hierarchical clustering. Medical Engineering and Physics 21/5:325-337, 1999.
8 Jovovic M., Attention, Memories and Behavioural Data-driven Study, Advances in Neurology and Neuroscience, 2019.