We are interested in Bell nolocality not only because the famous debate called EPR paradox, which was reiced by Albert Einstein and co-looker to show the in-completeness of the quantum theory. But because it is a very nice thought experiment that ca prove the working principle of the world— do we really have inerdeterminism in the world , or it’s determinisitic.

1. EPR paradox and “local realism”

1.1. The debate of EPR paradox

With the development of quantum theory, people start to believe that the theory to describe quantum physis should be intrisically statistival.

But some other group (e.g. Einstein) believed that a theory with stastistical laws should only be a temporary fix, and that determinism should be ultimately recovered.

• Einstein’s idea: (concept of most people)

  • Locality + realism 定域实在论

  • Locality: a object is influenced directly only by its immediate surroundings.

    • Example:

      transfer of information or energy cannot exceed the speed of light ← “special theory of relativity” 狭义相对论

  • Realism: physcial properties of objects exist independently of observation.

    • It assumes that particles have definite properties at all times, wether we observe it or not.

    • Einstein’s Example:

      the moon light will be there no matter you look at it or not.

    • Quantum measurement

• However, they don’t believed quantum machinics in a complete theory. (1947)
• This debate lasted for decades, until John Bell proposed an experimentally verifiable scheme in 1981.

1.2. Bell nonlocality

• Some explainations:

  • The basic idea of Bell nolocality:

    Design a game with two parties, when the two parties cannot communicate to collude on their results, we can tell that their experimental result cannot be explained by any classical theory based on local realism.

  • If we observe a violation of Bell game, we can falsify the explained based on “loacal realism”

  • For example:

    the “local hidden-variable” model

  • We have to accept that there are some “no-local” resources shared between the two parties.

• Bell nonlocality & quantum theory: Bell nonlocality is a field that is independent of quantum mechanics

  it’s not a speculation, not a notion mediated by a theory. It can be defined by its own and tested in its own.

• Application: Bell non-locality will help in quantum communication and quantum crypt

  • Bell theorm shows that there exists trace randomness in the world. Then naturally we are able to harvert such resources from Bell game. (This conclusion does not rely on the completeness or correctness of quantum theory)

  • Bell nonlocality provides the most compelling certification fo the correct functioning of some quantum devices, like those required by quantum communication and crpto:

    “Bell nonlocaltiy does not rely on the proper modeling of devices being used”——“Revice-independent”

2. Formalising Bell nonlocality