Completely top–down hierarchical structure in quantum mechanics

Yakir Aharonov*, Eliahu Cohen, Jeff Tollaksen

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Can a large system be fully characterized using its subsystems via inductive reasoning? Is it possible to completely reduce the behavior of a complex system to the behavior of its simplest “atoms”? In this paper we answer these questions in the negative for a specific class of systems and measurements. After a general introduction of the topic, we present the main idea with a simple two-particle example, where strong correlations arise between two apparently empty boxes. This leads to surprising effects within atomic and electromagnetic systems. A general construction based on pre-and postselected ensembles is then suggested, wherein the N-body correlation can be genuinely perceived as a global property, as long as one is limited to performing measurements which we term “strictly local.” We conclude that under certain boundary conditions, higher-order correlations within quantum mechanical systems can determine lower-order ones, but not vice versa. Surprisingly, the lower-order correlations provide no information whatsoever regarding the higher-order correlations. This supports a top–down structure in many-body quantum mechanics.

Original languageEnglish
Pages (from-to)11730-11735
Number of pages6
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number46
StatePublished - 13 Nov 2018


  • Emergence
  • Quantum mechanics
  • Reductionism
  • Top–down
  • Weak values


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