{"title":"基于计算复杂性的顺序和逆因果隐变量理论的禁区定理","authors":"Doriano Brogioli","doi":"arxiv-2409.11792","DOIUrl":null,"url":null,"abstract":"The celebrated Bell's no-go theorem rules out the hidden-variable theories\nfalling in the hypothesis of locality and causality, by requiring the theory to\nmodel the quantum correlation-at-a-distance phenomena. Here I develop an\nindependent no-go theorem, by inspecting the ability of a theory to model\nquantum \\emph{circuits}. If a theory is compatible with quantum mechanics, then\nthe problems of solving its mathematical models must be as hard as calculating\nthe output of quantum circuits, i.e., as hard as quantum computing. Rigorously,\nI provide complexity classes capturing the idea of sampling from sequential\n(causal) theories and from post-selection-based (retro-causal) theories; I show\nthat these classes fail to cover the computational complexity of sampling from\nquantum circuits. The result is based on widely accepted conjectures on the\nsuperiority of quantum computers over classical ones. The result represents a\nno-go theorem that rules out a large family of sequential and\npost-selection-based theories. I discuss the hypothesis of the no-go theorem\nand the possible ways to circumvent them. In particular, I discuss the Schulman\nmodel and its extensions, which is retro-causal and is able to model quantum\ncorrelation-at-a-distance phenomena: I provides clues suggesting that it\nescapes the hypothesis of the no-go theorem.","PeriodicalId":501226,"journal":{"name":"arXiv - PHYS - Quantum Physics","volume":"33 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A no-go theorem for sequential and retro-causal hidden-variable theories based on computational complexity\",\"authors\":\"Doriano Brogioli\",\"doi\":\"arxiv-2409.11792\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The celebrated Bell's no-go theorem rules out the hidden-variable theories\\nfalling in the hypothesis of locality and causality, by requiring the theory to\\nmodel the quantum correlation-at-a-distance phenomena. Here I develop an\\nindependent no-go theorem, by inspecting the ability of a theory to model\\nquantum \\\\emph{circuits}. If a theory is compatible with quantum mechanics, then\\nthe problems of solving its mathematical models must be as hard as calculating\\nthe output of quantum circuits, i.e., as hard as quantum computing. Rigorously,\\nI provide complexity classes capturing the idea of sampling from sequential\\n(causal) theories and from post-selection-based (retro-causal) theories; I show\\nthat these classes fail to cover the computational complexity of sampling from\\nquantum circuits. The result is based on widely accepted conjectures on the\\nsuperiority of quantum computers over classical ones. The result represents a\\nno-go theorem that rules out a large family of sequential and\\npost-selection-based theories. I discuss the hypothesis of the no-go theorem\\nand the possible ways to circumvent them. In particular, I discuss the Schulman\\nmodel and its extensions, which is retro-causal and is able to model quantum\\ncorrelation-at-a-distance phenomena: I provides clues suggesting that it\\nescapes the hypothesis of the no-go theorem.\",\"PeriodicalId\":501226,\"journal\":{\"name\":\"arXiv - PHYS - Quantum Physics\",\"volume\":\"33 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - PHYS - Quantum Physics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.11792\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - PHYS - Quantum Physics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.11792","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A no-go theorem for sequential and retro-causal hidden-variable theories based on computational complexity
The celebrated Bell's no-go theorem rules out the hidden-variable theories
falling in the hypothesis of locality and causality, by requiring the theory to
model the quantum correlation-at-a-distance phenomena. Here I develop an
independent no-go theorem, by inspecting the ability of a theory to model
quantum \emph{circuits}. If a theory is compatible with quantum mechanics, then
the problems of solving its mathematical models must be as hard as calculating
the output of quantum circuits, i.e., as hard as quantum computing. Rigorously,
I provide complexity classes capturing the idea of sampling from sequential
(causal) theories and from post-selection-based (retro-causal) theories; I show
that these classes fail to cover the computational complexity of sampling from
quantum circuits. The result is based on widely accepted conjectures on the
superiority of quantum computers over classical ones. The result represents a
no-go theorem that rules out a large family of sequential and
post-selection-based theories. I discuss the hypothesis of the no-go theorem
and the possible ways to circumvent them. In particular, I discuss the Schulman
model and its extensions, which is retro-causal and is able to model quantum
correlation-at-a-distance phenomena: I provides clues suggesting that it
escapes the hypothesis of the no-go theorem.