Relabelings/permutationsΒΆ

Permutations are specified by a string composed of relabelings of measurement outcomes, measurement settings and party permutations, in that order, separated by single spaces. Note that permutations acts as a right action on Bell expressions (see the Appendix of FaacetsPaper).

A relabeling of measurement outcomes is specified by writing the party and measurement setting affected first, using a letter and a number respectively, and then the permutation of outcomes itself using the cycle notation.

For example, the permutation of outcomes 1 and 2 for the third measurement setting of Alice is written A3(1,2).

A relabeling of measurement settings is specified by writing first the party letter and then permutation of settings in the cycle notation. The cyclic permutation of the three measurement settings of Alice is written A(1,2,3).

Permutation of parties is written in the cycle notation, using letters. For example, the permutation of Alice and Bob is written (A, B).

As an example, the generators of the symmetry group of the original CHSH inequality can be written as:

  • A1(1,2) A2(1,2) B1(1,2) B2(1,2) (permuting outcomes for all settings)
  • A2(1,2) B(1,2), B1(1,2) A(1,2) (permuting outcomes and settings at the same time)
  • A(1,2) B(1,2) (A,B) (permuting parties and settings).