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Sokolov B, Rossi MAC, García-Pérez G, Maniscalco S. Emergent entanglement structures and self-similarity in quantum spin chains. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2022; 380:20200421. [PMID: 35599560 DOI: 10.1098/rsta.2020.0421] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/07/2023]
Abstract
We introduce an experimentally accessible network representation for many-body quantum states based on entanglement between all pairs of its constituents. We illustrate the power of this representation by applying it to a paradigmatic spin chain model, the XX model, and showing that it brings to light new phenomena. The analysis of these entanglement networks reveals that the gradual establishment of quasi-long range order is accompanied by a symmetry regarding single-spin concurrence distributions, as well as by instabilities in the network topology. Moreover, we identify the existence of emergent entanglement structures, spatially localized communities enforced by the global symmetry of the system that can be revealed by model-agnostic community detection algorithms. The network representation further unveils the existence of structural classes and a cyclic self-similarity in the state, which we conjecture to be intimately linked to the community structure. Our results demonstrate that the use of tools and concepts from complex network theory enables the discovery, understanding and description of new physical phenomena even in models studied for decades. This article is part of the theme issue 'Emergent phenomena in complex physical and socio-technical systems: from cells to societies'.
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Affiliation(s)
- Boris Sokolov
- QTF Centre of Excellence, Department of Physics, Faculty of Science, University of Helsinki, Helsinki, Finland
- Algorithmiq Ltd, Kanavakatu 3C, Helsinki 00160, Finland
- InstituteQ - the Finnish Quantum Institute, University of Helsinki, Finland
| | - Matteo A C Rossi
- Algorithmiq Ltd, Kanavakatu 3C, Helsinki 00160, Finland
- QTF Centre of Excellence, Center for Quantum Engineering, Department of Applied Physics, Aalto University School of Science, Aalto 00076, Finland
- InstituteQ - the Finnish Quantum Institute, Aalto University, Finland
| | - Guillermo García-Pérez
- QTF Centre of Excellence, Department of Physics, Faculty of Science, University of Helsinki, Helsinki, Finland
- Algorithmiq Ltd, Kanavakatu 3C, Helsinki 00160, Finland
- InstituteQ - the Finnish Quantum Institute, University of Helsinki, Finland
- Complex Systems Research Group, Department of Mathematics and Statistics, University of Turku, Turun Yliopisto 20014, Finland
| | - Sabrina Maniscalco
- QTF Centre of Excellence, Department of Physics, Faculty of Science, University of Helsinki, Helsinki, Finland
- Algorithmiq Ltd, Kanavakatu 3C, Helsinki 00160, Finland
- InstituteQ - the Finnish Quantum Institute, University of Helsinki, Finland
- QTF Centre of Excellence, Center for Quantum Engineering, Department of Applied Physics, Aalto University School of Science, Aalto 00076, Finland
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Revisiting Born’s Rule through Uhlhorn’s and Gleason’s Theorems. ENTROPY 2022; 24:e24020199. [PMID: 35205494 PMCID: PMC8871054 DOI: 10.3390/e24020199] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Subscribe] [Scholar Register] [Received: 12/07/2021] [Revised: 01/20/2022] [Accepted: 01/26/2022] [Indexed: 11/16/2022]
Abstract
In a previous article we presented an argument to obtain (or rather infer) Born’s rule, based on a simple set of axioms named “Contexts, Systems and Modalities" (CSM). In this approach, there is no “emergence”, but the structure of quantum mechanics can be attributed to an interplay between the quantized number of modalities that is accessible to a quantum system and the continuum of contexts that are required to define these modalities. The strong link of this derivation with Gleason’s theorem was emphasized, with the argument that CSM provides a physical justification for Gleason’s hypotheses. Here, we extend this result by showing that an essential one among these hypotheses—the need of unitary transforms to relate different contexts—can be removed and is better seen as a necessary consequence of Uhlhorn’s theorem.
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