Detector-Frame Quantum Limits for Heterodyne Timing in Relativistic Optical Links

Abstract

Long-baseline optical links for space interferometry and satellite quantum networks rely on heterodyne phase tracking under Doppler motion and gravitational frequency shifts. These relativistic shifts can generate large detector-frame beat-frequency offsets over finite readout windows and thereby constrain the temporal precision of front-end phase readout. We develop a detector-frame framework for this problem using an effective two-mode signal--local-oscillator model in which relativistic motion rescales the local-oscillator frequency. Within this setting we derive closed-form Mandelstam--Tamm and Margolus--Levitin bounds for representative Gaussian resources and connect global state distinguishability with the operational precision of heterodyne phase tracking. In the bright-local-oscillator regime we identify a geometric--operational mismatch: the joint optical state can evolve on arbitrarily short global timescales while the relevant information rate is set by the measured detector record. Combining this result with an open-loop transient-acquisition analysis, we show that white phase noise and relativistic beat-frequency drift that is approximately constant over the acquisition window generate a cube-root scaling benchmark for the optimal pre-lock open-loop integration window and the minimum residual phase error. These results establish detector-frame benchmarks for quantum-limited heterodyne timing in relativistic optical links and clarify how global dynamical bounds enter task-restricted continuous optical measurements.

36 pages, 1 figure. Published in Advanced Quantum Technologies

References in corpus (28)

• Gaussian Quantum Information
• Quantum metrology
• Satellite-to-ground quantum key distribution
• The Unruh effect and its applications
• Detection of 15 dB Squeezed States of Light and their Application for the Absolute Calibration of Photoelectric Quantum Efficiency
• The maximum speed of dynamical evolution
• Quantum speed limits: from Heisenberg's uncertainty principle to optimal quantum control
• Squeezed states of light and their applications in laser interferometers
• 30 years of squeezed light generation
• Quantum limits to dynamical evolution
• Advances in Space Quantum Communications
• Quantum fidelity for arbitrary Gaussian states
• Quantum interferometric visibility as a witness of general relativistic proper time
• Fundamental Quantum Limit to Waveform Estimation
• Fundamental quantum optics experiments conceivable with satellites -- reaching relativistic distances and velocities
• Fidelity for displaced squeezed states and the oscillator semigroup
• Spacetime effects on satellite-based quantum communications
• Relativistic Quantum Metrology: Exploiting relativity to improve quantum measurement technologies
• Readout for intersatellite laser interferometry: Measuring low frequency phase fluctuations of HF signals with microradian precision
• Space-Ground Coherent Optical links: Ground Receiver Performance With Adaptive Optics and Digital Phase-Locked Loop
• Adapting time-delay interferometry for LISA data in frequency
• Characterization of photoreceivers for LISA
• General relativistic laser interferometric observables of the GRACE-Follow-On mission
• Enhanced Frequency noise suppression for LISA by combining cavity and arm locking control systems
• Frequency planning for LISA
• Free Space Optical Frequency Comparison Over Rapidly Moving Links
• Quantum-enhanced optical phase-insensitive heterodyne detection beyond 3-dB noise penalty of image band
• Relativistic Quantum-Speed Limit for Gaussian Systems and Prospective Experimental Verification