Towards a Fisher-Information Description of Complexity in de Sitter Universe
Abstract
:1. Introduction
2. MERA/de Sitter Correspondence
3. Fisher Information Measure = Gravitational Action
4. Complexity Interpreted as FIM
5. Complexity Interpreted as Norm FIM
5.1. Testing in Gravity
5.2. FIM as Candidates of Complexity
6. Conclusions and Discussion
Author Contributions
Funding
Conflicts of Interest
Appendix A. Fisher Information Measure: A Brief Review
Appendix B. Remarks on the Quantum Circuit
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1. | The reason we choose element gate like this is that the MERA network can be thought of as an iterative compression algorithm that maps the density matrix of an interval to a direct product state [13]. In the opposite direction, this tensor network maps a non-entangled state to an entangled state [33]. Then each of the element quantum gates acts on the simplest entanglement pair (2-qubit). The simplest toy example of gate set we choose may be shown in Appendix B. |
2. | In this paper we set . In general, one should associate a prefactor where is a positive number. The undetermined prefactor is only determined by the choice of gate set and Hamiltonian locality. We have already claimed above that for MERA the chosen gates are simple. Hence for a system whose Hamiltonian locality equal to quantum-gate locality, we expect Appendix B. The prefactor is precisely the same as the one obtained for the AdS black holes [17,18]. |
3. | In general for a system with N degrees of freedom, the concept of scrambling time that describes how long a perturbation spreads over d.o.f. This concept is only valid for systems with [18]. |
Theory | Lagrangian | Estimation Error | Lloyd’s Bound |
---|---|---|---|
Einstein Gravity | R | Obey | |
Gravity | Obey |
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Chen, C.-B.; Shu, F.-W. Towards a Fisher-Information Description of Complexity in de Sitter Universe. Universe 2019, 5, 221. https://doi.org/10.3390/universe5120221
Chen C-B, Shu F-W. Towards a Fisher-Information Description of Complexity in de Sitter Universe. Universe. 2019; 5(12):221. https://doi.org/10.3390/universe5120221
Chicago/Turabian StyleChen, Chong-Bin, and Fu-Wen Shu. 2019. "Towards a Fisher-Information Description of Complexity in de Sitter Universe" Universe 5, no. 12: 221. https://doi.org/10.3390/universe5120221
APA StyleChen, C. -B., & Shu, F. -W. (2019). Towards a Fisher-Information Description of Complexity in de Sitter Universe. Universe, 5(12), 221. https://doi.org/10.3390/universe5120221