Custom Bell inequalities from formal sums of squares

Understand

Bell inequalities play a key role in certifying quantum properties for device-independent quantum information protocols.

• It is still a major challenge, however, to devise Bell inequalities tailored for an arbitrary given quantum state.
• Existing approaches based on sums of squares provide results in this direction, but they are restricted by the necessity of first choosing measurement settings suited to the state.
• Here, we show how the sum of square property can be enforced for an arbitrary target state by making an appropriate choice of nullifiers, which is made possible by leaving freedom in the choice of measurement.