Quantum speed limit for mixed states using an experimentally realizable metric

Here, we introduce a new metric for non-degenerate density operator evolving along unitary orbit and show that this is experimentally realizable operation dependent metric on the quantum state space. Using this metric, we obtain the geometric uncertainty relation that leads to a new quantum speed limit (QSL). We also obtain a Margolus-Levitin bound and an improved Chau bound for mixed states. We propose how to measure this new distance and speed limit in quantum interferometry. Finally, we also generalize the QSL for completely positive trace preserving evolutions.