Quantum bounds and device-independent security with rank-one qubit measurements
arXiv:2503.13282 · doi:10.1038/s41534-025-01175-x
Abstract
Device-independent (DI) quantum protocols exploit Bell inequality violations to ensure security or certify quantum properties without making assumptions about the internal workings of the devices. In this work, we study the role of rank-one qubit positive operator-valued measures (POVMs) in DI scenarios. This class includes all qubit extremal POVMs, i.e., those measurements that cannot be realized by randomly choosing among others, as well as part of non-extremal POVMs, which have recently been shown to be useful for security applications in sequential quantum protocols. We demonstrate that any rank-one POVM can generate correlations in bipartite scenarios that saturate a Tsirelson inequality, i.e., a quantum bound on linear combinations of outcome statistics, when the two parties share an arbitrary entangled two-qubit state and some other self-tested measurements are performed. For extremal POVMs, such saturation allows for an explicit calculation of the guessing probability and the worst-case conditional von Neumann entropy. From the Tsirelson inequality, we establish a randomness certification method that facilitates numerical simulations and noise analysis. To test its feasibility, we performed a proof-of-concept experiment employing a three-outcome POVM on tilted entangled states under experimental non-idealities. We further explore the case of non-extremal POVMs, providing insights into their role in DI protocols.
arXiv commentv2: updated to match the published version
References in corpus (25)
- Bell nonlocality
- Random Numbers Certified by Bell's Theorem
- A convergent hierarchy of semidefinite programs characterizing the set of quantum correlations
- Bounding the set of quantum correlations
- Self-testing of quantum systems: a review
- Randomness vs Non Locality and Entanglement
- Sum-of-squares decompositions for a family of CHSH-like inequalities and their application to self-testing
- Classical randomness in quantum measurements
- Advances in device-independent quantum key distribution
- Geometry of the set of quantum correlations
- Optimal randomness certification from one entangled bit
- Self-testing of Pauli observables for device-independent entanglement certification
- Mutually unbiased bases and symmetric informationally complete measurements in Bell experiments
- Security of device-independent quantum key distribution protocols: a review
- Device-Independent Certification of a Nonprojective Qubit Measurement
- A framework for quantum-secure device-independent randomness expansion
- Experimental Test of Sequential Weak Measurements for Certified Quantum Randomness Extraction
- Device-independent lower bounds on the conditional von Neumann entropy
- Maximal randomness from partially entangled states
- Extremal Quantum Correlations and Cryptographic Security
- Generalized self-testing and the security of the 6-state protocol
- Device-independent certification of two bits of randomness from one entangled bit and Gisin's elegant Bell inequality
- Self-testing of any pure entangled state with minimal number of measurements and optimal randomness certification in one-sided device-independent scenario
- Device-independent certification of maximal randomness from pure entangled two-qutrit states using non-projective measurements
- Secure and robust randomness with sequential quantum measurements