L. Davidovich

General framework for estimating the ultimate precision limit in noisy quantum-enhanced metrology

Quantum strategies can help to make parameter-estimation schemes more precise, but for noisy processes it is typically not known how large that improvement may be. Here, a universal quantum bound is derived for the error in the estimation of parameters that characterize dynamical processes.

Open-system dynamics of entanglement:a key issues review

One of the greatest challenges in the fields of quantum information processing and quantum technologies is the detailed coherent control over each and every constituent of quantum systems with an ever increasing number of particles. Within this endeavor, harnessing of many-body entanglement against the detrimental effects of the environment is a major pressing issue. Besides being an important concept from a fundamental standpoint, entanglement has been recognized as a crucial resource for quantum speed-ups or performance enhancements over classical methods. Understanding and controlling many-body entanglement in open systems may have strong implications in quantum computing, quantum simulations of many-body systems, secure quantum communication or cryptography, quantum metrology, our understanding of the quantum-to-classical transition, and other important questions of quantum foundations.In this paper we present an overview of recent theoretical and experimental efforts to underpin the dynamics of entanglement under the influence of noise. Entanglement is thus taken as a dynamic quantity on its own, and we survey how it evolves due to the unavoidable interaction of the entangled system with its surroundings. We analyze several scenarios, corresponding to different families of states and environments, which render a very rich diversity of dynamical behaviors.In contrast to single-particle quantities, like populations and coherences, which typically vanish only asymptotically in time, entanglement may disappear at a finite time. In addition, important classes of entanglement display an exponential decay with the number of particles when subject to local noise, which poses yet another threat to the already-challenging scaling of quantum technologies. Other classes, however, turn out to be extremely robust against local noise. Theoretical results and recent experiments regarding the difference between local and global decoherence are summarized. Control and robustness-enhancement techniques, scaling laws, statistical and geometrical aspects of multipartite-entanglement decay are also reviewed; all in order to give a broad picture of entanglement dynamics in open quantum systems addressed to both theorists and experimentalists inside and outside the field of quantum information.

Experimental investigation of the dynamics of entanglement: Sudden death, complementarity, and continuous monitoring of the environment

We report on an experimental investigation of the dynamics of entanglement between a single qubit and its environment, as well as for pairs of qubits interacting independently with individual environments, using photons obtained from parametric down-conversion. The qubits are encoded in the polarizations of single photons, while the interaction with the environment is implemented by coupling the polarization of each photon with its momentum. A convenient Sagnac interferometer allows for the implementation of several decoherence channels and for the continuous monitoring of the environment. For an initially entangled photon pair, one observes the vanishing of entanglement before coherence disappears. For a single qubit interacting with an environment, the dynamics of the complementarity relations connecting single-qubit properties and its entanglement with the environment is experimentally determined. The evolution of a single qubit under continuous monitoring of the environment is investigated, demonstrating that a qubit may decay even when the environment is found in the unexcited state. This implies that entanglement can be increased by local continuous monitoring, which is equivalent to entanglement distillation. We also present a detailed analysis of the transfer of entanglement from the two-qubit system to the two corresponding environments, between which entanglement may suddenly appear, and show instances for which no entanglement is created between dephasing environments, nor between either of them and the corresponding qubit: the initial two-qubit entanglement gets transformed into legitimate multiqubit entanglement of the Greenberger-Horne-Zeilinger type.

Scaling Laws for the Decay of Multiqubit Entanglement

We investigate the decay of entanglement of generalized N-particle Greenberger-Horne-Zeilinger (GHZ) states interacting with independent reservoirs. Scaling laws for the decay of entanglement and for its finite-time extinction (sudden death) are derived for different types of reservoirs. The latter is found to increase with N. However, entanglement becomes arbitrarily small, and therefore useless as a resource, much before it completely disappears, around a time which is inversely proportional to the number of particles. We also show that the decay of multiparticle GHZ states can generate bound entangled states.

Quantum Speed Limit for Physical Processes

The evaluation of the minimal evolution time between two distinguishable states of a system is important for assessing the maximal speed of quantum computers and communication channels. Lower bounds for this minimal time have been proposed for unitary dynamics. Here we show that it is possible to extend this concept to nonunitary processes, using an attainable lower bound that is connected to the quantum Fisher information for time estimation. This result is used to delimit the minimal evolution time for typical noisy channels.

Direct measurement of finite-time disentanglement induced by a reservoir

We propose a method for directly probing the dynamics of disentanglement of an initial two-qubit entangled state under the action of a reservoir. We show that it is possible to detect disentanglement, for experimentally realizable examples of decaying systems, through the measurement of a single observable, which is invariant throughout the decay. The systems under consideration may lead to either finite-time or asymptotic disentanglement. A general prescription for measuring this observable, which yields an operational meaning to entanglement measures, is proposed, and exemplified for cavity quantum electrodynamics and trapped ions.

Generation of Einstein-Podolsky-Rosen-Entangled Radiation through an Atomic Reservoir

We propose a scheme for generating two-mode squeezing in high-Q resonators using a beam of atoms with random arrival times, which acts as a reservoir for the field. The scheme is based on four-wave mixing processes leading to emission into two cavity modes, which are resonant with the Rabi sidebands of the atomic dipole transition, driven by a saturating classical field. At steady state the cavity modes are in an Einstein-Podolsky-Rosen state, whose degree of entanglement is controlled by the intensity and the frequency of the transverse field. This scheme is robust against stochastic fluctuations in the atomic beam, does not require atomic detection nor velocity selection, and can be realized by presently available experimental setups with microwave resonators.

Determining the Dynamics of Entanglement

Evolving Entanglement Quantum mechanical entanglement is a powerful but fragile resource for quantum information processing. It lends itself to increased computational power over classical computers. However, when quantum systems interact with their environment, which they must do if you want to follow what they are doing, then the entanglement can be lost. Jiménez Farías et al. (p. 1414, published online 14 May) present an experimental and theoretical study on entangled photon pairs, showing that they can determine and understand how the entanglement evolves as the system interacts with its surroundings. The evolution of quantum mechanically entangled photon pairs can now be measured as they interact with their environment. The estimation of the entanglement of multipartite systems undergoing decoherence is important for assessing the robustness of quantum information processes. It usually requires access to the final state and its full reconstruction through quantum tomography. General dynamical laws may simplify this task. We found that when one of the parties of an initially entangled two-qubit system is subject to a noisy channel, a single universal curve describes the dynamics of entanglement for both pure and mixed states, including those for which entanglement suddenly disappears. Our result, which is experimentally demonstrated using a linear optics setup, leads to a direct and efficient determination of entanglement through the knowledge of the initial state and single-party process tomography alone, foregoing the need to reconstruct the final state.

Quantum Metrological Limits via a Variational Approach

The minimum achievable statistical uncertainty in the estimation of physical parameters is determined by the quantum Fisher information. Its computation for noisy systems is still a challenging problem. Using a variational approach, we present an equation for obtaining the quantum Fisher information, which has an explicit dependence on the mathematical description of the noise. This method is applied to obtain a useful analytical bound to the quantum precision in the estimation of phase-shifts under phase diffusion, which shows that the estimation uncertainty cannot be smaller than a noise-dependent constant.

Sub-Planck phase-space structures and Heisenberg-limited measurements

We show how sub-Planck phase-space structures in the Wigner function [W. H. Zurek, Nature (London) 412, 712 (2001)] can be used to achieve Heisenberg-limited sensitivity in weak-force measurements. Nonclassical states of harmonic oscillators, consisting of superpositions of coherent states, are shown to be useful for the measurement of weak forces that cause translations or rotations in phase space, which is done by entangling the quantum oscillator with a two-level system. Implementations of this strategy in cavity QED and ion traps are described.