{
  "id": "1611.09101",
  "version": "v1",
  "published": "2016-11-28T13:13:37.000Z",
  "updated": "2016-11-28T13:13:37.000Z",
  "title": "Quantum Theory and Local Hidden Variable Theory: General Features and Tests for EPR Steering and Bell Non-locality",
  "authors": [
    "Bryan J Dalton",
    "Margaret D Reid"
  ],
  "comment": "Version 1. 68 pages, 2 figures",
  "categories": [
    "quant-ph"
  ],
  "abstract": "Quantum states for bipartite composite systems are categorised as either separable or entangled, but the states can also be divided differently into Bell local or Bell non-local states. Bell states are where the probability P(a,b|A,B,c) for measured outcomes a, b on sub-system observables A, B for state preparation process c, is given by a local hidden variable theory (LHVT) form P(a,b|A,B,c)=Sum{h}P(h|c)P(a|A,c,h)P(b|B,c,h) (where preparation c results in a probability distribution P(h|c) for hidden variables h, P(a|A,c,h), P(b|B,c,h) are probabilities for measured outcome a,b on sub-system observable A,B when the hidden variables are h. Quantum states where P(a,b|A,B,c) is not given by a LHVT form are Bell non-local and lead to Bell inequality violation experiments. For the Bell local states there are three cases depending on whether both, one of or neither of the sub-system LHVT probabilities are also given by a quantum probability involving sub-system density operators. Cases where one or both are given by a quantum probability are known as local hidden states (LHS) and such states are non-steerable. The steerable states are the Bell local states where there is no LHS, or the Bell non-local states. In a previous paper tests for entanglement for two mode systems involving identical massive bosons were obtained. In the present paper we consider tests for EPR steering and Bell non-locality in such systems. We find that spin squeezing in the any spin component, a weak correlation test, the Hillery-Zubairy spin variance test and a two mode quadrature squeezing test all show that the LHS model fails, and hence the quantum state is steerable. We also find a strong correlation test and a stronger version of the Hillery-Zubairy spin variance test also show that EPR steering occurs. In addition we find a new test for Bell non-locality that applies for spin operator measurements.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-11-28T13:13:37.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "local hidden variable theory",
      "bell non-locality",
      "epr steering",
      "hillery-zubairy spin variance test",
      "general features"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 68,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}