Quantum metrology exploits quantum mechanical laws to improve the precision in estimating technologically relevant parameters such as phase, frequency, or magnetic fields. Probe states are usually tailored to the particular dynamics whose parameters are being estimated. Here we consider a novel framework where quantum estimation is performed in an interferometric configuration, using bipartite probe states prepared when only the spectrum of the generating Hamiltonian is known. We introduce a figure of merit for the scheme, given by the worst-case precision over all suitable Hamiltonians, and prove that it amounts exactly to a computable measure of discord-type quantum correlations for the input probe. We complement our theoretical results with a metrology experiment, realized in a highly controllable room-temperature nuclear magnetic resonance setup, which provides a proof-of-concept demonstration for the usefulness of discord in sensing applications. Discordant probes are shown to guarantee a nonzero phase sensitivity for all the chosen generating Hamiltonians, while classically correlated probes are unable to accomplish the estimation in a worst-case setting. This work establishes a rigorous and direct operational interpretation for general quantum correlations, shedding light on their potential for quantum technology. All quantitative sciences benefit from the spectacular developments in high-accuracy devices, such as atomic clocks, gravitational wave detectors, and navigation sensors. Quantum metrology studies how to harness quantum mechanics to gain precision in estimating quantities not amenable to direct observation [1][2][3][4][5]. The phase estimation paradigm with measurement schemes based on an interferometric setup [6] encompasses a broad and relevant class of metrology problems, which can be conveniently cast in terms of an input-output scheme [1]. An input probe state ρ AB enters a two-arm channel, in which the reference subsystem B is unaffected while subsystem A undergoes a local unitary evolution, so that the output density matrix can be written as ρ, where φ is the parameter we wish to estimate and H A is the local Hamiltonian generating the unitary dynamics. Information on φ is then recovered through an estimator functionφ constructed upon possibly joint measurements of suitable dependent observables performed on the output ρ φ AB . For any input state ρ AB and generator H A , the maximum achievable precision is determined theoretically by the quantum Cramér-Rao bound [3]. Given repetitive interrogations via ν identical copies of ρ AB , this fundamental relation sets a lower limit to the mean square error Var ρ φ AB ðφÞ that measures the statistical distance betweenφ and φ, Var ρ φ AB ðφÞ ≥ ½νFðρ AB ; H A Þ −1 , where F is the quantum Fisher information (QFI) [7], which quantifies how much information about φ is encoded in ρ φ AB . The inequality is asymptotically tight as ν → ∞, provided the most informative quantum measurement is carried out at the output stage. Using this quantity as a figu...

The attempt to gain a theoretical understanding of the concept of time in quantum mechanics has triggered significant progress towards the search for faster and more efficient quantum technologies. One of such advances consists in the interpretation of the time-energy uncertainty relations as lower bounds for the minimal evolution time between two distinguishable states of a quantum system, also known as quantum speed limits. We investigate how the non uniqueness of a bona fide measure of distinguishability defined on the quantum state space affects the quantum speed limits and can be exploited in order to derive improved bounds. Specifically, we establish an infinite family of quantum speed limits valid for unitary and nonunitary evolutions, based on an elegant information geometric formalism. Our work unifies and generalizes existing results on quantum speed limits, and provides instances of novel bounds which are tighter than any established one based on the conventional quantum Fisher information. We illustrate our findings with relevant examples, demonstrating the importance of choosing different information metrics for open system dynamics, as well as clarifying the roles of classical populations versus quantum coherences, in the determination and saturation of the speed limits. Our results can find applications in the optimization and control of quantum technologies such as quantum computation and metrology, and might provide new insights in fundamental investigations of quantum thermodynamics.Comment: 17 pages, 8 figures. Close to published versio

The quantification of quantum correlations (other than entanglement) usually entails labored numerical optimization procedures also demanding quantum state tomographic methods. Thus it is interesting to have a laboratory friendly witness for the nature of correlations. In this Letter we report a direct experimental implementation of such a witness in a room temperature nuclear magnetic resonance system. In our experiment the nature of correlations is revealed by performing only few local magnetization measurements. We also compared the witness results with those for the symmetric quantum discord and we obtained a fairly good agreement.