Quantum metrology with boundary time crystals

Quantum sensing can outperform classical strategies but typically suffers from noise and decoherence. We show that decoherence-driven many-body systems exhibiting dissipative phase transitions—specifically boundary time crystals (BTCs), where time-translational symmetry is broken and persistent oscillations appear in open systems at the thermodynamic limit—enable quantum-enhanced sensitivity. Focusing on a collectively driven-dissipative large-spin model, we demonstrate that the transition from a symmetry-unbroken to a BTC phase (a second-order transition) features enhanced sensitivity quantified by the quantum Fisher information (QFI). Through finite-size scaling we determine critical exponents and their relations, confirming the second-order nature of the transition. Practically, the scheme leverages decoherence, is initialization independent, and achieves enhanced precision with a simple collective spin measurement.