Quantum Speed Limit

Quantum speed limits (QSLs) define the minimum time required for a quantum system to evolve between distinguishable states, placing fundamental bounds on control, sensing, and information processing. In this project, we advance the theory of QSLs across multiple physical regimes.

We begin by incorporating relativistic corrections and higher-order energy-momentum expansions to explore how coherent and squeezed quantum states evolve under modified dynamics. These refinements have direct implications for high-precision quantum metrology, particularly in scenarios where Doppler and gravitational redshifts are significant, such as gravitational wave detectors (e.g., LIGO and LISA) and satellite-based quantum communication systems.

We further extend the QSL framework to irreversible quantum systems, including the inverted harmonic oscillator, uncovering novel bounds on evolution speed that are intrinsically linked to entropy production and the exponential divergence of trajectories. These findings provide valuable insights into fundamental processes such as information scrambling in black holes, particle production in cosmology, and strong-field quantum phenomena.

We also demonstrate the operational realization of QSLs in classical wave systems. By emulating quantum-limited evolution through classical optics, we enable analog simulations of unstable quantum dynamics, ultrafast beam shaping, and high-sensitivity parameter estimation.

In addition, we investigate quantum gravimetry using optically levitated nanoparticles. By explicitly incorporating gravitational acceleration and time into the Hamiltonian framework, we derive two-parameter quantum Fisher information bounds, thereby improving the theoretical sensitivity limits of inertial quantum sensors.

Lastly, we also examine QSLs in the context of quantum reference frames (QRFs), where the reference frame itself is treated as a quantum system. This line of inquiry seeks to understand how QRF-dependent descriptions constrain evolution speed and impact the calibration of relativistic quantum sensors.