The CHSH-type inequalities for infinite-dimensional quantum systems
Yu Guo
TL;DR
This paper extends CHSH inequalities to infinite-dimensional quantum systems, showing they serve as necessary and sufficient conditions for pure state separability and relate to distillability, similar to two-qubit systems.
Contribution
The paper develops CHSH-type inequalities for infinite-dimensional systems and demonstrates their equivalence to entanglement criteria, paralleling two-qubit results.
Findings
CHSH inequalities are necessary and sufficient for pure state separability in infinite dimensions
Violating Bell inequalities implies the state is distillable
CHSH operators satisfy Cirel'son inequalities in infinite-dimensional systems
Abstract
By establishing CHSH operators and CHSH-type inequalities, we show that any entangled pure state in infinite-dimensional systems is entangled in a subspace. We find that, for infinite-dimensional systems, the corresponding properties are similar to that of the two-qubit case: (i) The CHSH-type inequalities provide a sufficient and necessary condition for separability of pure states; (ii) The CHSH operators satisfy the Cirel'son inequalities; (iii) Any state which violates one of these Bell inequalities is distillable.
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