Certifying Sets of Quantum Observables with Any Full-Rank State.

Area of Science:

• Quantum Information Science
• Foundations of Quantum Mechanics

Background:

• Quantum contextuality is a key feature of quantum mechanics, distinguishing it from classical physics.
• Certification of quantum devices is crucial for secure quantum communication and computation.

Purpose of the Study:

• To introduce and validate a novel method for certifying quantum systems.
• To establish a connection between contextuality witnesses and Bell self-testing.

Main Methods:

• Utilizing sequential measurements on quantum systems.
• Analyzing statistics from experiments with any full-rank initial state, including mixed and thermal states.
• Proving the equivalence between complete Kochen-Specker sets and the possibility of Bell self-testing via CFR.

Main Results:

• Demonstrated that unique sets of quantum observables with state-independent contextuality witnesses can be certified using any full-rank initial state.
• Established the feasibility and robustness of "certification with any full-rank state" (CFR) for quantum systems with dimensions d≥3, particularly useful in dimensions 3 and 4.
• Proved that complete Kochen-Specker sets enable Bell self-testing if and only if they allow for CFR.

Conclusions:

• CFR provides a powerful and versatile tool for certifying quantum devices.
• A fundamental link exists between contextuality-based certification and Bell self-testing.
• The findings open new avenues for combining certification methods in quantum experiments.