Operationally Admissible Post-Quantum Correlations from a Standard Quantum Walk

TL;DR

This paper demonstrates that a standard quantum walk can produce post-quantum correlations through extended preparations, with observable violations influenced by measurement coarse-graining.

Contribution

It reveals how standard quantum walks can generate and emulate post-quantum correlations via extended coin preparations without modifying the walk dynamics.

Findings

Quantum walks can produce CHSH violations exceeding Tsirelson's bound.

Extended coin preparations enable emulation of post-quantum correlations.

Coarse-grained measurements can suppress observable Bell violations.

Abstract

It is shown that a standard one-dimensional coined discrete-time quantum walk can generate operationally admissible post-quantum correlations in a coin-position Bell scenario, without any modification of its unitary nearest-neighbor dynamics. Post-quantum features enter exclusively through an extended operational preparation of the coin, described by a complementarity-violating Hermitian trace-one operator, while physical consistency is enforced solely at the level of observable statistics via admissibility and no-signaling. The extended preparation admits an experimental emulation through a two-component quasiprobability reconstruction over physical coin states, at the price of an increased sampling overhead. The walk-generated coin-position entanglement can support CHSH values exceeding Tsirelson's bound, even though the walk dynamics remains fully standard. We also show that physically natural coarse-grained position measurements can render such post-quantum correlations operationally inaccessible, strongly suppressing observable Bell violations. The purpose here is to contrast the separation between the existence of post-quantum behavior and its accessibility under realistic measurement constraints.