Quantum sensing is one of the arenas that exemplifies the superiority of quantum technologies over their classical counterparts. Such superiority, however, can be diminished due to unavoidable noise and decoherence of the probe. Thus, metrological strategies to fight against or profit from decoherence are highly desirable. This is the case of certain types of decoherence-driven many-body systems supporting dissipative phase transitions, which might be helpful for sensing. Boundary time crystals are exotic dissipative phases of matter in which the time-translational symmetry is broken, and long-lasting oscillations emerge in open quantum systems at the thermodynamic limit. We show that the transition from a symmetry unbroken into a boundary time crystal phase, described by a second-order transition, reveals quantum-enhanced sensitivity quantified through quantum Fisher information. We also determine the critical exponents of the system and establish their relationship. Our scheme is indeed a demonstration of harnessing decoherence for achieving quantum-enhanced sensitivity. From a practical perspective, it has the advantage of being independent of initialization and can be captured by a simple measurement.

量子传感是体现量子技术相对于传统技术的优越性的领域之一。然而，由于不可避免的噪声和探头的退相干，这种优势可能会被削弱。因此，非常需要对抗退相干或从退相干中获益的计量策略。这是某些类型的退相干驱动的多体系统支持耗散相变的情况，这可能有助于传感。边界时间晶体是物质的奇异耗散相，其中时间平移对称性被打破，并且在热力学极限的开放量子系统中出现持久振荡。我们证明，从对称性未破缺到边界时间晶相的转变（由二阶转变描述）揭示了通过量子费希尔信息量化的量子增强灵敏度。我们还确定系统的关键指数并建立它们的关系。我们的方案确实证明了利用退相干来实现量子增强灵敏度。从实用的角度来看，它的优点是独立于初始化，并且可以通过简单的测量来捕获。