Certified Private Relational Time from Entanglement

Area of Science:

• Quantum Information Science
• Foundations of Physics
• Quantum Metrology

Background:

• Classical timekeeping relies on local, independent clocks.
• Quantum entanglement offers non-classical correlations with potential for novel applications.
• Previous work explored quantum correlations but lacked operational time definitions.

Purpose of the Study:

• To define time operationally using discrete measurement registrations on an entangled singlet state.
• To investigate the relational (coincidence-tick) stream as a quantum resource.
• To compare quantum predictions for synchronized events against classical models and explore device-independent privacy.

Main Methods:

• Utilizing a singlet state for time definition, with local tick rates fixed by unbiased marginals.
• Operationally defining a joint tick record by exchanging time tags and outcomes, identifying synchronized events (the ++ channel).
• Comparing the coincidence tick rate R(θ) to a local-hidden-variable model Rcl(θ)=θ/(2π) and performing Bell tests.

Main Results:

• The quantum prediction for the coincidence tick rate exceeds the classical benchmark for obtuse analyzer separations, with a maximal relative excess of ~13.6% near θ≈140.5°.
• Demonstrated that "faster ticking" refers to the rate of identified coincidence ticks, not local clock improvements.
• Outlined a method for "Certified Private Time" using multiple settings and Bell tests for device-independent privacy certification.

Conclusions:

• Entangled clocks provide a novel operational definition of time based on quantum correlations.
• Quantum mechanics predicts a higher rate of synchronized events compared to classical models under specific conditions.
• The framework enables device-independent certification of privacy for relational time-stamping, analogous to certified randomness.