Given a binary linear code C with parameters [n,k]_2, a coset state is simply a logical or error state of the quantum error-correcting code CSS(C',C) for some code C \subseteq C'. Information stored in quantum coset states can be highly entangled among constituent qubits, and may be undetectable with only local, individual-qubit measurements. Consequently, detecting coset states locally, even when measurement outcomes are aggregated, is generally infeasible. While entanglement prevents local detection of coset states, it enables local measurements to be correlated in highly non-classical ways. In this talk, we discuss a quantum non-local game in which two players each receive half of a random coset state.

We will focus on aspects of the game relating to coding theory, including: 1) How is the entanglement structure of the coset state determined by the underlying code, 2) What types of correlations (classical vs. quantum) are observed for different codes, and 3) What types of codes allow players to output guesses which are simultaneously correct or incorrect, without learning anything about the underlying coset state.

Based in part on joint work with N. Swanson and E. Soljanin.

arXiv: https://arxiv.org/abs/2410.08160