toqito.nonlocal_games.ExtendedNonlocalGame already handles standard extended nonlocal games, but it does not yet have a way to represent the constrained variant studied in Escolà-Farràs and Speelman, Lossy-and-Constrained Extended Non-Local Games with Applications to Quantum Cryptography (arXiv:2405.13717).
I do not want this issue to turn into "implement the whole paper." The target here is much narrower:
- add support for linear constraints on answer events in the SDP upper-bound routine for extended nonlocal games;
- use that support to reproduce the constrained BB84 monogamy-of-entanglement example from the paper.
Relevant code:
What should be added:
- a way to specify linear constraints on answer-event probabilities for an
ExtendedNonlocalGame;
- support for those constraints in the SDP upper-bound path;
- at least one helper or test fixture for the constrained BB84 game from the paper;
- regression tests covering the constrained BB84 case.
Suggested scope:
- it is fine to limit this to the upper-bound SDP path for now;
- it is fine if the initial interface is fairly simple, as long as it is documented and testable;
- do not try to solve the full lossy case in this issue.
Acceptance criteria:
- existing extended nonlocal game tests continue to pass;
- the new constrained BB84 tests pass;
- the implementation reproduces the expected unconstrained BB84 value as a sanity check;
- the PR explains clearly how the paper’s constraints were translated into the
toqito SDP formulation.
Out of scope:
- full lossy-and-constrained game support;
- reproducing every application from the paper;
- refactoring unrelated nonlocal game code.
A good PR for this issue should include a short note pointing to the part of the paper being implemented and explaining the mapping from the paper’s notation to the variables used in toqito.
toqito.nonlocal_games.ExtendedNonlocalGamealready handles standard extended nonlocal games, but it does not yet have a way to represent the constrained variant studied in Escolà-Farràs and Speelman, Lossy-and-Constrained Extended Non-Local Games with Applications to Quantum Cryptography (arXiv:2405.13717).I do not want this issue to turn into "implement the whole paper." The target here is much narrower:
Relevant code:
ExtendedNonlocalGame.commuting_measurement_value_upper_boundWhat should be added:
ExtendedNonlocalGame;Suggested scope:
Acceptance criteria:
toqitoSDP formulation.Out of scope:
A good PR for this issue should include a short note pointing to the part of the paper being implemented and explaining the mapping from the paper’s notation to the variables used in
toqito.