Quantum mechanics predicts that measurements of incompatible observables carry a minimum uncertainty which is independent of technical deficiencies of the measurement apparatus or incomplete knowledge of the state of the system. Nothing yet seems to prevent a single physical quantity, such as one spin component, from being measured with arbitrary precision. Here we show that an intrinsic quantum uncertainty on a single observable is ineludible in a number of physical situations. When revealed on local observables of a bipartite system, such uncertainty defines an entire class of bona fide measures of nonclassical correlations. For the case of 2 x d systems, we find that a unique measure is defined, which we evaluate in closed form. We then discuss the role that these correlations, which are of the 'discord' type, can play in the context of quantum metrology. We show in particular that the amount of discord present in a bipartite mixed probe state guarantees a minimum precision, as quantified by the quantum Fisher information, in the optimal phase estimation protocol.Comment: Published in PRL, Editors' Suggestio

Quantum coherence is the key resource for quantum technology, with applications in quantum optics, information processing, metrology and cryptography. Yet, there is no universally efficient method for quantifying coherence either in theoretical or in experimental practice. I introduce a framework for measuring quantum coherence in finite dimensional systems. I define a theoretical measure which satisfies the reliability criteria established in the context of quantum resource theories. Then, I present an experimental scheme implementable with current technology which evaluates the quantum coherence of an unknown state of a d-dimensional system by performing two programmable measurements on an ancillary qubit, in place of the O(d 2 ) direct measurements required by full state reconstruction. The result yields a benchmark for monitoring quantum effects in complex systems, e.g. certifying non-classicality in quantum protocols and probing the quantum behaviour of biological complexes. Introduction -While harnessing quantum coherence is matter of routine in delivering quantum technology [1][2][3][4][5], and the quantum optics rationale rests on creation and manipulation of coherence [6], there is no universally efficient route to measure the amount of quantum coherence carried by the state of a system in dimension d > 2. It is customary to employ quantifiers tailored to the scenario of interest, i.e. of not general employability, expressed in terms of ad hoc entropic functions, correlators, or functions of the off-diagonal density matrix coefficients (if available) [7][8][9]. Quantum information theory provides the framework to address the problem. Physical laws are interpreted as restrictions on the accessible quantum states and operations, while the properties of physical systems are the resources that one must consume to perform a task under such laws [10]. An algorithmic characterization of quantum coherence as a resource and a set of bona fide criteria for coherence monotones have been identified [7, 11, 12]. Also, coherence has been shown to be related to the asymmetry of a quantum state [13, 14]. On the experimental side, the scalability of the detection scheme is a major criterion in developing witnesses and measures of coherence, as we are interested in exploring the quantum features of highly complex macrosystems, e.g. multipartite quantum registers and networks. Therefore, it is desirable to have a coherence measure which is both theoretically sound and experimentally appealing.

Recent results in quantum information theory characterize quantum coherence in the context of resource theories. Here, we study the relation between quantum coherence and quantum discord, a kind of quantum correlation which appears even in nonentangled states. We prove that the creation of quantum discord with multipartite incoherent operations is bounded by the amount of quantum coherence consumed in its subsystems during the process. We show how the interplay between quantum coherence consumption and creation of quantum discord works in the preparation of multipartite quantum correlated states and in the model of deterministic quantum computation with one qubit.

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...