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Certified Private Quantum Time Ticks Away Faster than Any Classical Clock

Karl Svozil

TL;DR

The paper introduces the Entangled Clock, where time is operationally defined by discrete ticks from singlet-state measurements and synchronization is quantified by the joint ticking rate R(θ). Quantum predictions yield R_QM(θ) = (1/2) sin^2(θ/2), which matches classical predictions at θ = 0, π/2, and π but surpasses them near θ ≈ 2.45 rad, with a maximum excess Δ(θ) ≈ 0.053 (about 13.6%) relative to the classical bound. This faster ticking is attributed to contextuality and the cosine-law quantum correlations, which cannot be captured by counterfactual-free classical models and relate to CHSH-type Bell violations. The work then extends these ideas to Certified Private Time, proposing a device-independent-like protocol that certifies private, in situ time streams via measurement-context dependence and seed expansion, and discusses practical experimental considerations and resistance to playback attacks. Collectively, the results establish a quantum metrology of time that not only beats a natural classical benchmark in a specific regime but also provides a pathway to sovereign temporal frameworks grounded in Bell-nonlocality and contextuality.

Abstract

We introduce the concept of an entangled clock, where the flow of time is operationally defined by the discrete registration of measurement outcomes on a singlet state. Comparing the synchronization rate of two such clocks against classical models, we find that at obtuse relative angles, the quantum clock ticks strictly faster than this classical benchmark. We further propose a protocol for Certified Private Time, adapting device-independent randomness certification to the temporal domain; this guarantees a sovereign timeline that ticks away faster than any local realistic mechanism allows.

Certified Private Quantum Time Ticks Away Faster than Any Classical Clock

TL;DR

The paper introduces the Entangled Clock, where time is operationally defined by discrete ticks from singlet-state measurements and synchronization is quantified by the joint ticking rate R(θ). Quantum predictions yield R_QM(θ) = (1/2) sin^2(θ/2), which matches classical predictions at θ = 0, π/2, and π but surpasses them near θ ≈ 2.45 rad, with a maximum excess Δ(θ) ≈ 0.053 (about 13.6%) relative to the classical bound. This faster ticking is attributed to contextuality and the cosine-law quantum correlations, which cannot be captured by counterfactual-free classical models and relate to CHSH-type Bell violations. The work then extends these ideas to Certified Private Time, proposing a device-independent-like protocol that certifies private, in situ time streams via measurement-context dependence and seed expansion, and discusses practical experimental considerations and resistance to playback attacks. Collectively, the results establish a quantum metrology of time that not only beats a natural classical benchmark in a specific regime but also provides a pathway to sovereign temporal frameworks grounded in Bell-nonlocality and contextuality.

Abstract

We introduce the concept of an entangled clock, where the flow of time is operationally defined by the discrete registration of measurement outcomes on a singlet state. Comparing the synchronization rate of two such clocks against classical models, we find that at obtuse relative angles, the quantum clock ticks strictly faster than this classical benchmark. We further propose a protocol for Certified Private Time, adapting device-independent randomness certification to the temporal domain; this guarantees a sovereign timeline that ticks away faster than any local realistic mechanism allows.

Paper Structure

This paper contains 16 sections, 13 equations, 2 figures.

Table of Contents

  1. Introduction
  2. The Entangled Clock Protocol
  3. Operational Time and Zeilinger's Principle
  4. Synchronized Time
  5. Classical Simulation: Peres' Bomb
  6. Comparison: When Quantum Clocks Tick Faster
  7. The Cardinal Regimes
  8. The Anomalous Regime
  9. Contextuality and Unperformed Experiments
  10. Certifying Quantumness
  11. Experimental Considerations
  12. Certified Private Time
  13. The Memory-Stick Clock
  14. Protocol for Time Certification
  15. Escaping the Block Universe
  16. ...and 1 more sections

Figures (2)

  • Figure 1: Comparison of the quantum ($R_{QM}$, solid blue) and classical ($R_{cl}$, dashed red) synchronization rates as functions of the relative detector angle $\theta$. The curves coincide at $\theta = 0, \pi/2, \pi$ but diverge maximally at $\theta_2 \approx 140.5^\circ$, where the quantum clock "ticks faster."
  • Figure 2: The synchronization excess $\Delta(\theta) = R_{QM} - R_{cl}$. The quantum clock lags at acute angles ($\theta_1 \approx 39.5^\circ$) but leads at obtuse angles ($\theta_2 \approx 140.5^\circ$).