Device-independent bounds for Hardy's experiment

TL;DR

This paper derives a device-independent quantum bound for Hardy's nonlocality test, showing it matches two-qubit system results and identifying the specific states that achieve this maximum, with implications for experimental implementations.

Contribution

It provides a dimension-independent bound for Hardy's test and characterizes the states that attain this maximum, establishing Hardy's test as a self-test protocol.

Findings

Maximum violation matches two-qubit systems

Only specific states achieve the maximum violation

Higher-dimensional systems do not offer advantages in experiments

Abstract

In this Letter we compute an analogue of Tsirelson's bound for Hardy's test of nonlocality, that is, the maximum violation of locality constraints allowed by the quantum formalism, irrespective of the dimension of the system. The value is found to be the same as the one achievable already with two-qubit systems, and we show that only a very specific class of states can lead to such maximal value, thus highlighting Hardy's test as a device-independent self-test protocol for such states. By considering realistic constraints in Hardy's test, we also compute device-independent upper bounds on this violation and show that these bounds are saturated by two-qubit systems, thus showing that there is no advantage in using higher-dimensional systems in experimental implementations of such test.