{
  "id": "2303.12819",
  "version": "v1",
  "published": "2023-03-22T14:57:08.000Z",
  "updated": "2023-03-22T14:57:08.000Z",
  "title": "Quantum space-time marginal problem: global causal structure from local causal information",
  "authors": [
    "Zhian Jia",
    "Minjeong Song",
    "Dagomir Kaszlikowski"
  ],
  "comment": "v1: 17 pages, comments welcome",
  "categories": [
    "quant-ph",
    "gr-qc"
  ],
  "abstract": "Spatial and temporal quantum correlations can be unified in the framework of the pseudo-density operators, and quantum causality between the involved events in an experiment is encoded in the corresponding pseudo-density operator. We study the relationship between local causal information and global causal structure. A space-time marginal problem is proposed to infer global causal structures from given marginal causal structures where causal structures are represented by the pseudo-density operators; we show that there almost always exists a solution in this case. By imposing the corresponding constraints on this solution set, we could obtain the required solutions for special classes of marginal problems, like a positive semidefinite marginal problem, separable marginal problem, etc. We introduce a space-time entropy and propose a method to determine the global causal structure based on the maximum entropy principle, which can be solved effectively by using a neural network. The notion of quantum pseudo-channel is also introduced and we demonstrate that the quantum pseudo-channel marginal problem can be solved by transforming it into a pseudo-density operator marginal problem via the channel-state duality.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-03-22T14:57:08.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "global causal structure",
      "quantum space-time marginal problem",
      "local causal information",
      "pseudo-density operator marginal problem",
      "quantum pseudo-channel marginal problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}