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We provide a thermodynamic task to certify the general quantum resources of both states and channels via work extraction, showing that general quantum resources provide advantages in work extraction. Such work extraction tasks can be further applied to certify quantum entanglement in a one-sided device-independent way. As an application, we report a novel type of anomalous energy flow -- a type of locally extractable energy that is attributed to the globally distributed entanglement. Finally, we show that the existence of this novel anomalous energy flow is equivalent to measurement incompatibility., Comment: 5+3 pages; 1 figure

Bounding the optimal precision in parameter estimation tasks is of central importance for technological applications. In the regime of a small number of measurements, or that of low signal-to-noise ratios, the meaning of common frequentist bounds such as the Cram\'er-Rao bound (CRB) become questionable. Here, we discuss different linear (Barankin-like) conditions that can be imposed on estimators and analyze when these conditions admit an optimal estimator with finite variance, for any number of measurement repetitions. We show that, if the number of imposed conditions is larger than the number of measurement outcomes, there generally does not exist a corresponding estimator with finite variance. We analyze this result from different viewpoints and examples and elaborate on connections to the shot-noise limit and the Kitaev phase estimation algorithm. We then derive an extended Cram\'er-Rao bound that is compatible with a finite variance in situations where the Barankin bound is undefined. Finally, we show an exemplary numerical confrontation between frequentist and Bayesian approaches to parameter estimation.

We show how quantum correlations allow us to break the local speed limits of physical processes using only local measurements and classical communication between two parties that share an entangled state. Inequalities that bound the minimal time of evolution of a quantum state by energy fluctuations can be violated in the presence of steering by conditioning on the measurement outcomes of a remote system. Our results open up new pathways for studying how quantum correlations influence the dynamical properties of states and observables.

Entanglement and non-Gaussianity are physical resources that are essential for a large number of quantum-optics protocols. Non-Gaussian entanglement is indispensable for quantum-computing advantage and outperforms its Gaussian counterparts in a number of quantum-information protocols. The characterization of non-Gaussian entanglement is a critical matter as it is in general highly demanding in terms of resources. We propose a simple protocol based on the Fisher information for witnessing entanglement in an important class of non-Gaussian entangled states: photon-subtracted states. We demonstrate that our protocol is relevant for the detection of non-Gaussian entanglement generated by multiple photon-subtraction and that it is experimentally feasible through homodyne detection., Comment: We have corrected errors found in Figures 8 and 9 of the previous version and improved the manuscript with an analysis of the entanglement produced by multi-photon subtraction. We have adapted the main text, abstract and title correspondingly. 16 pages, 14 figures

Superresolution is one of the key issues at the crossroads of contemporary quantum optics and metrology. Recently, it was shown that for an idealized case of two balanced sources, spatial mode demultiplexing (SPADE) achieves resolution better than direct imaging even in the presence of measurement crosstalk [Phys. Rev. Lett. 125, 100501 (2020)]. In this work, we consider arbitrarily unbalanced sources and provide a systematic analysis of the impact of crosstalk on the resolution obtained from SPADE. As we dissect, in this generalized scenario, SPADE's effectiveness depends non-trivially on the strength of crosstalk, relative brightness and the separation between the sources. In particular, for any source imbalance, SPADE performs worse than ideal direct imaging in the asymptotic limit of vanishing source separations. Nonetheless, for realistic values of crosstalk strength, SPADE is still the superior method for several orders of magnitude of source separations., Comment: 10 pages, 6 figures

We show that a significant quantum gain corresponding to squeezed or over-squeezed spin states can be obtained in multiparameter estimation by measuring the Hadamard coefficients of a 1D or 2D signal. The physical platform we consider consists of twolevel atoms in an optical lattice in a squeezed-Mott configuration, or more generally by correlated spins distributed in spatially separated modes. Our protocol requires the possibility to locally flip the spins, but relies on collective measurements. We give examples of applications to scalar or vector field mapping and compressed sensing.

We determine analytically the quantum Cram\'er-Rao bound for the estimation of the separation between two point sources in arbitrary Gaussian states. Our analytical expression is valid for arbitrary sources brightness, and it allows to determine how different resources, such as mutual coherence (induced by thermal correlations or displacement) or squeezing affect the scaling of the ultimate resolution limit with the mean number of emitted photons. In practical scenarios, we find coherent states of the sources to achieve quantum optimal resolution., Comment: 5 pages, 3 figures, comments are welcome!

Quantum optical metrology aims to identify ultimate sensitivity bounds for the estimation of parameters encoded into quantum states of the electromagnetic field. In many practical applications, including imaging, microscopy, and remote sensing, the parameter of interest is not only encoded in the quantum state of the field, but also in its spatio-temporal distribution, i.e. in its mode structure. In this mode-encoded parameter estimation setting, we derive an analytical expression for the quantum Fisher information valid for arbitrary multimode Gaussian fields. To illustrate the power of our approach, we apply our results to the estimation of the transverse displacement of a beam and to the temporal separation between two pulses. For these examples, we show how the estimation sensitivity can be enhanced by adding squeezing into specific modes., Comment: 20 pages (14 main + 6 appendices), 3 figures. Sec. 4 rewritten to include a completely new set of examples that were not in v1. Comments are very welcome!

Quantum correlations are at the core of current developments in quantum technologies. Certification protocols of entanglement and steering, suitable for continuous-variable non-Gaussian states are scarce and generally highly demanding from an experimental point of view. We propose a protocol based on Fisher information for witnessing steering in general continuous-variable bipartite states, through homodyne detection. It proves to be relevant for the detection of non-Gaussian steering in scenarios where witnesses based on Gaussian features like the covariance matrix are shown to fail., Comment: 14 pages, 14 figures, comments are welcome!

We identify the multiparameter sensitivity of split nonclassical spin states, such as spin-squeezed and Dicke states spatially distributed into several addressable modes. Analytical expressions for the spin-squeezing matrix of a family of states that are accessible by current atomic experiments reveal the quantum gain in multiparameter metrology, as well as the optimal strategies to maximize the sensitivity. We further study the mode entanglement of these states by deriving a witness for genuine $k$-partite mode entanglement from the spin-squeezing matrix. Our results highlight the advantage of mode entanglement for distributed sensing, and outline optimal protocols for multiparameter estimation with nonclassical spatially-distributed spin ensembles., Comment: Comments are welcome

Quantum light is described not only by a quantum state but also by the shape of the electromagnetic modes on which the state is defined. Optical precision measurements often estimate a ``mode parameter'' that determines properties such as frequency, temporal shape and the spatial distribution of the light field. By deriving quantum precision limits, we establish the fundamental bounds for mode parameter estimation. Our results reveal explicit mode-design recipes that enable the estimation of any mode parameter with quantum enhanced precision. Our approach provides practical methods for optimizing mode parameter estimation with relevant applications, including spatial and temporal positioning, spectroscopy, phase estimation, and superresolution imaging., Comment: 5 + 11 pages

In an ensemble of two-level atoms that can be described in terms of a collective spin, entangled states can be used to enhance the sensitivity of interferometric precision measurements. While non-Gaussian spin states can produce larger quantum enhancements than spin-squeezed Gaussian states, their use requires the measurement of observables that are nonlinear functions of the three components of the collective spin. In this paper we develop strategies that achieve the optimal quantum enhancements using non-Gaussian states produced by a nonlinear one-axis-twisting Hamiltonian, and show that measurement-after-interaction techniques, known to amplify the output signals in quantum parameter estimation protocols, are effective in measuring nonlinear spin observables. Including the presence of the relevant decoherence processes from atomic experiments, we determine analytically the quantum enhancement of non-Gaussian over-squeezed states as a function of the noise parameters for arbitrary atom numbers.

We analyze the problem of resolving two point-sources in the case of mutually coherent sources with arbitrary quantum statistics, mutual phase, relative and absolute intensity. We use a sensitivity measure based on the method of moments and compare direct imaging with spatial mode demultiplexing, analytically proving the advantage of the latter. We show that the sensitivity of spatial mode demultiplexing saturates the quantum Fisher information, for all known cases, even for non-Gaussian states of the sources.

We show how preparation uncertainty relations that are formulated as sums of variances may be tightened by using the quantum Fisher information to quantify quantum fluctuations. We apply this to derive stronger angular momentum uncertainty relations, which in the case of spin-$1/2$ turn into equalities involving the purity. Using an analogy between pure-state decompositions in the Bloch sphere and the moment of inertia of rigid bodies, we identify optimal decompositions that achieve the convex- and concave-roof decomposition of the variance. Finally, we illustrate how these results may be used to identify the classical and quantum limits on phase estimation precision with an unknown rotation axis., Comment: 11 pages, 5 figures. See also the related work by G. T\'oth and F. Fr\"owis, Phys. Rev. Research 4, 013075 (2022)

We propose a remote phase sensing scheme inspired by the high sensitivity of the entanglement produced by coherent multimode photon addition on the phase set in the remote heralding apparatus. By exploring the case of delocalized photon addition over two modes containing identical coherent states, we derive the optimal observable to perform remote phase estimation from heralded quadrature measurements. The technique is experimentally tested with calibration measurements and then used for estimating a remote phase with a sensitivity that is found to scale with the intensity of the (local) coherent states, which never interacted with the sample., Comment: 8 pages, 6 figures. Includes a Supplemental Material section

We derive inequalities sufficient to detect the genuine $N$-partite steering of $N$ distinct systems. Here, we are careful to distinguish between the concepts of full $N$-partite steering inseparability (where steering is confirmed individually for all bipartitions of the $N$ systems, thus negating the bilocal hidden state model for each bipartition) and genuine $N$-partite steering (which excludes all convex combinations of the bilocal hidden state models). Other definitions of multipartite steering are possible and we derive inequalities to detect a stricter genuine $N$-partite steering based on only one trusted site. The inequalities are expressed as variances of quadrature phase amplitudes and thus apply to continuous variable systems. We show how genuine $N$-partite steerable states can be created and detected for the nodes of a network formed from a single-mode squeezed state passed through a sequence of $N-1$ beam splitters. A stronger genuine $N$-partite steering is created, if one uses two squeezed inputs, or $N$ squeezed inputs. We are able to confirm that genuine tripartite steering (by the above definition and the stricter definition) has been realised experimentally. Finally, we analyze how bipartite steering and entanglement is distributed among the systems in the tripartite case, illustrating with monogamy inequalities. While we use Gaussian states to benchmark the criteria, the inequalities derived in this paper are not based on the assumption of Gaussian states, which gives advantage for quantum communication protocols.

Steering criteria are conditions whose violation excludes the possibility of describing the observed measurement statistics with local hidden state (LHS) models. When the available data do not allow to exclude arbitrary LHS models, it may still be possible to exclude LHS models with a specific separability structure. Here, we derive experimentally feasible criteria that put quantitative bounds on the multipartite entanglement of LHS. Our results reveal that separable states may contain hidden entanglement that can be unlocked by measurements on another system, even if no steering between the two systems is possible.

We present an experimentally practical method to reveal Einstein-Podolsky-Rosen steering in non-Gaussian spin states by exploiting a connection to quantum metrology. Our criterion is based on the quantum Fisher information, and uses bounds derived from generalized spin-squeezing parameters that involve measurements of higher-order moments. This leads us to introduce the concept of conditional spin-squeezing parameters, which quantify the metrological advantage provided by conditional states, as well as detect the presence of an EPR paradox.

Sensitivity limits are usually determined using the Cram\'er-Rao bound. Recently this approach has been used to obtain the ultimate resolution limit for the estimation of the separation between two incoherent point sources. However, methods that saturate these resolution limits, usually require the full measurement statistics, which can be challenging to access. In this work, we introduce a simple superresolution protocol to estimate the separation between two thermal sources which relies only on the average value of a single accessible observable. We show how optimal observables for this technique may be constructed for arbitrary thermal sources, and we study their sensitivities when one has access to spatially resolved intensity measurements (direct imaging) and photon counting after spatial mode demultiplexing. For demultiplexing, our method is optimal, i.e. it saturates the quantum Cram\'er-Rao bound. We also investigate the impact of noise on the optimal observables, their measurement sensitivity and on the scaling with the number of detected photons of the smallest resolvable separation. For low signals in the image plane, we demonstrate that our method saturates the Cram\'er-Rao bound even in the presence of noise., Comment: 18 pages, 12 figures, 1 table. Comments are very welcome!

Recent works identified resolution limits for the distance between incoherent point sources. However, it remains unclear how to choose suitable observables and estimators to reach these limits in practical situations. Here, we show how estimators saturating the Cram\'er-Rao bound for the distance between two thermal point sources can be constructed using an optimally designed observable in the presence of practical imperfections, such as misalignment, crosstalk and detector noise., Comment: 6 pages, 4 figures. Comments are welcome

We characterize metrologically useful multipartite entanglement by representing partitions with Young diagrams. We derive entanglement witnesses that are sensitive to the shape of Young diagrams and show that Dyson's rank acts as a resource for quantum metrology. Common quantifiers, such as the entanglement depth and $k$-separability are contained in this approach as the diagram's width and height. Our methods are experimentally accessible in a wide range of atomic systems, as we illustrate by analyzing published data on the quantum Fisher information and spin-squeezing coefficients., Comment: 6 + 7 pages, 5 + 8 figures

Excited-state quantum phase transitions (ESQPTs) extend the notion of quantum phase transitions beyond the ground state. They are characterized by closing energy gaps amid the spectrum. Identifying order parameters for ESQPTs poses however a major challenge. We introduce spinor Bose-Einstein condensates as a versatile platform for studies of ESQPTs. Based on the mean-field dynamics, we define a topological order parameter that distinguishes between excited-state phases, and discuss how to interferometrically access the order parameter in current experiments. Our work opens the way for the experimental characterization of excited-state quantum phases in atomic many-body systems., Comment: 14 pages, 3 figures

The Einstein-Podolsky-Rosen (EPR) paradox plays a fundamental role in our understanding of quantum mechanics, and is associated with the possibility of predicting the results of non-commuting measurements with a precision that seems to violate the uncertainty principle. This apparent contradiction to complementarity is made possible by nonclassical correlations stronger than entanglement, called steering. Quantum information recognises steering as an essential resource for a number of tasks but, contrary to entanglement, its role for metrology has so far remained unclear. Here, we formulate the EPR paradox in the framework of quantum metrology, showing that it enables the precise estimation of a local phase shift and of its generating observable. Employing a stricter formulation of quantum complementarity, we derive a criterion based on the quantum Fisher information that detects steering in a larger class of states than well-known uncertainty-based criteria. Our result identifies useful steering for quantum-enhanced precision measurements and allows one to uncover steering of non-Gaussian states in state-of-the-art experiments., Comment: Comments are welcome!

Superresolution techniques based on intensity measurements after a spatial mode decomposition can overcome the precision of diffraction-limited direct imaging. However, realistic measurement devices always introduce finite crosstalk in any such mode decomposition. Here, we show that any nonzero crosstalk leads to a breakdown of superresolution when the number $N$ of detected photons is large. Combining statistical and analytical tools, we obtain the scaling of the precision limits for weak, generic crosstalk from a device-independent model as a function of the crosstalk probability and $N$. The scaling of the smallest distance that can be distinguished from noise changes from $N^{-1/2}$ for an ideal measurement to $N^{-1/4}$ in the presence of crosstalk., Comment: 5 + 6 pages, 5 + 3 figures

A comprehensive description of molecular electron transfer reactions is essential for our understanding of fundamental phenomena in bio-energetics and molecular electronics. Experimental studies of molecular systems in condensed-phase environments, however, face difficulties to independently control the parameters that govern the transfer mechanism with high precision. We show that trapped-ion experiments instead allow to reproduce and continuously connect vastly different regimes of molecular charge transfer through precise tuning of, e.g., phonon temperature, electron-phonon interactions, and electronic couplings. Such a setting allows not only to reproduce widely-used transport models, such as Marcus theory. It also provides access to transfer regimes that are unattainable for molecular experiments, while controlling and measuring the relevant observables on the level of individual quanta. Our numerical simulations predict an unconventional quantum transfer regime, featuring a transition from quantum adiabatic- to resonance-assisted transfer as a function of the donor-acceptor energy gap, that can be reached by increasing the electronic coupling at low temperatures. Trapped ion-based quantum simulations thus promise to enhance our microscopic understanding of molecular electron transfer processes, and may help to reveal efficient design principles for synthetic devices., Comment: 11 pages, 6 figures

Entanglement witnesses based on first and second moments exist in the form of spin-squeezing criteria for the detection of particle entanglement from collective measurements, and in form of modified uncertainty relations for the detection of mode entanglement or steering. By revealing a correspondence between them, we show that metrologically useful spin squeezing reveals multimode entanglement in symmetric spin states that are distributed into addressable modes. We further derive tight state-independent multipartite entanglement bounds on the spin-squeezing coefficient and point out their connection to widely-used entanglement criteria that depend on the state's polarization. Our results are relevant for state-of-the-art experiments where symmetric entangled states are distributed into a number of addressable modes, such as split spin-squeezed Bose-Einstein condensates., Comment: comments are welcome

Squeezing currently represents the leading strategy for quantum enhanced precision measurements of a single parameter in a variety of continuous- and discrete-variable settings and technological applications. However, many important physical problems including imaging and field sensing require the simultaneous measurement of multiple unknown parameters. The development of multiparameter quantum metrology is yet hindered by the intrinsic difficulty in finding saturable sensitivity bounds and feasible estimation strategies. Here, we derive the general operational concept of multiparameter squeezing, identifying metrologically useful states and optimal estimation strategies. When applied to spin- or continuous-variable systems, our results generalize widely-used spin- or quadrature-squeezing parameters. Multiparameter squeezing provides a practical and versatile concept that paves the way to the development of quantum-enhanced estimation of multiple phases, gradients, and fields, and for the efficient characterization of multimode quantum states in atomic and optical sensor networks., Comment: 8 + 10 pages, 4 + 1 figures

In a three-particle extension of Wheeler's delayed choice gedanken experiment, the quantum statistics of two particles is undetermined until a third particle is measured. As a function of the measurement result, the particles behave either as bosons or as fermions. The particles are distinguishable if no measurement is performed at all or when the measurement is performed in a rotated basis. The scheme is based on Greenberger-Horne-Zeilinger quantum correlations. It can be interpreted more generally as the encryption of maximally entangled states in a larger quantum superposition. The local quantum information is scrambled but can be decoded by the measurement result of a control particle. This can be extended to multiple particles and allows to develop quantum information protocols whose successful implementation depends on the collaboration of all parties., Comment: 9 pages, 3 figures

We consider the problem of quantum phase estimation with access to arbitrary measurements in a single suboptimal basis. The achievable sensitivity limit in this case is determined by the classical Cram\'{e}r-Rao bound with respect to the fixed basis. Here we show that the sensitivity can be enhanced beyond this limit if knowledge about the energy expectation value is available. The combined information is shown to be equivalent to a direct measurement of an optimal linear combination of the basis projectors and the phase-imprinting Hamiltonian. Application to an atomic clock with oversqueezed spin states yields a sensitivity gain that scales linearly with the number of atoms. Our analysis further reveals that small modifications of the observable can have a strong impact on the sensitivity., Comment: 7 pages, 1 figure

How can we detect that our local, controllable quantum system is correlated with some other inaccessible environmental system? The local detection method developed in recent years allows to realize a dynamical witness for correlations without requiring knowledge of or access to the environment that is correlated with the local accessible quantum system. Here, we provide a brief summary of the theoretical method and recent experimental studies with single photons and trapped ions coupled to increasingly complex environments., Comment: 12 pages, 3 figures

The well known metrological linear squeezing parameters (such as quadrature or spin squeezing) efficiently quantify the sensitivity of Gaussian states. Yet, these parameters are insufficient to characterize the much wider class of highly sensitive non-Gaussian states. Here, we introduce a class of metrological nonlinear squeezing parameters obtained by analytical optimization of measurement observables among a given set of accessible (possibly nonlinear) operators. This allows for the metrological characterization of non-Gaussian quantum states of discrete and continuous variables. Our results lead to optimized and experimentally-feasible recipes for high-precision moment-based estimation of a phase parameter and can be used to systematically construct multipartite entanglement and non-classicality witnesses for complex quantum states., Comment: 6+2 pages, 1 figure

Non-vanishing fluctuations of the vacuum state are a salient feature of quantum theory. These fluctuations fundamentally limit the precision of quantum sensors. Nowadays, several systems such as optical clocks, gravitational wave detectors, matter-wave interferometers, magnetometers, and optomechanical systems approach measurement sensitivities where the effect of quantum fluctuations sets a fundamental limit, the so-called standard quantum limit (SQL). It has been proposed that the SQL can be overcome by squeezing the vacuum fluctuations. Realizations of this scheme have been demonstrated in various systems. However, protocols based on squeezed vacuum crucially rely on precise control of the relative orientation of the squeezing with respect to the operation imprinting the measured quantity. Lack of control can lead to an amplification of noise and reduces the sensitivity of the device. Here, we experimentally demonstrate a novel quantum metrological paradigm based on phase insensitive Fock states of the motional state of a trapped ion, with applications in frequency metrology and displacement detection. The measurement apparatus is used in two different experimental settings probing non-commuting observables with sensitivities beyond the SQL. In both measurements, classical preparation and detection noise are sufficiently small to preserve the quantum gain in a full metrological protocol.

We identify precision limits for the simultaneous estimation of multiple parameters in multimode interferometers. Quantum strategies to enhance the multiparameter sensitivity are based on entanglement among particles, modes or combining both. The maximum attainable sensitivity of particle-separable states defines the multiparameter shot-noise limit, which can be surpassed without mode entanglement. Further enhancements up to the multiparameter Heisenberg limit are possible by adding mode entanglement. Optimal strategies which saturate the precision bounds are provided., Comment: 6 pages, 1 figure + Supplementary Material

Frequentist and Bayesian phase estimation strategies lead to conceptually different results on the state of knowledge about the true value of the phase shift. We compare the two frameworks and their sensitivity bounds to the estimation of an interferometric phase shift limited by quantum noise, considering both the cases of a fixed and a fluctuating parameter. We point out that frequentist precision bounds, such as the Cram\`er-Rao bound, for instance, do not apply to Bayesian strategies and vice-versa. Similarly, bounds for fluctuating parameters make no statement about the estimation of a fixed parameter., Comment: 4 figures

Understanding the distribution of quantum entanglement over many parties is a fundamental challenge of quantum physics and is of practical relevance for several applications in the field of quantum information. Here we use methods from quantum metrology to microscopically characterize the entanglement structure of multimode continuous-variable states in all possible multi-partitions and in all reduced distributions. From experimentally measured covariance matrices of Gaussian states with 2, 3, and 4 photonic modes with controllable losses, we extract the metrological sensitivity as well as an upper separability bound for each partition. An entanglement witness is constructed by comparing the two quantities. Our analysis demonstrates the usefulness of these methods for continuous-variable systems and provides a detailed geometric understanding of the robustness of cluster-state entanglement under photon losses.

The controlled generation and identification of quantum correlations, usually encoded in either qubits or continuous degrees of freedom, builds the foundation of quantum information science. Recently, more sophisticated approaches, involving a combination of two distinct degrees of freedom have been proposed to improve on the traditional strategies. Hyperentanglement describes simultaneous entanglement in more than one distinct degree of freedom, whereas hybrid entanglement refers to entanglement shared between a discrete and a continuous degree of freedom. In this work we propose a scheme that allows to combine the two approaches, and to extend them to the strongest form of quantum correlations. Specifically, we show how two identical, initially separated particles can be manipulated to produce Bell nonlocality among their spins, among their momenta, as well as across their spins and momenta. We discuss possible experimental realizations with atomic and photonic systems., Comment: 6 pages, 3 figures

We analyze families of measures for the quantum statistical speed which include as special cases the quantum Fisher information, the trace speed, i.e., the quantum statistical speed obtained from the trace distance, and more general quantifiers obtained from the family of Schatten norms. These measures quantify the statistical speed under generic quantum evolutions and are obtained by maximizing classical measures over all possible quantum measurements. We discuss general properties, optimal measurements, and upper bounds on the speed of separable states. We further provide a physical interpretation for the trace speed by linking it to an analog of the quantum Cram\'{e}r-Rao bound for median-unbiased quantum phase estimation., Comment: 19 pages, 1 figure

We introduce a multi-mode squeezing coefficient to characterize entanglement in $N$-partite continuous-variable systems. The coefficient relates to the squeezing of collective observables in the $2N$-dimensional phase space and can be readily extracted from the covariance matrix. Simple extensions further permit to reveal entanglement within specific partitions of a multipartite system. Applications with nonlinear observables allow for the detection of non-Gaussian entanglement., Comment: 11 pages, 2 figures

The resource theory of quantum coherence studies the off-diagonal elements of a density matrix in a distinguished basis, whereas the resource theory of purity studies all deviations from the maximally mixed state. We establish a direct connection between the two resource theories, by identifying purity as the maximal coherence which is achievable by unitary operations. The states that saturate this maximum identify a universal family of maximally coherent mixed states. These states are optimal resources under maximally incoherent operations, and thus independent of the way coherence is quantified. For all distance-based coherence quantifiers the maximal coherence can be evaluated exactly, and is shown to coincide with the corresponding distance-based purity quantifier. We further show that purity bounds the maximal amount of entanglement and discord that can be generated by unitary operations, thus demonstrating that purity is the most elementary resource for quantum information processing., Comment: 8+3 pages, 2 figures, published version

We formulate a general family of entanglement criteria for multipartite systems. Fisher information criteria compare the sensitivity to unitary rotations with the variances of suitable local observables. Generalized squeezing-type criteria provide lower bounds that are less stringent but only require measurements of second moments. The enhancement due to local access to the individual subsystems is studied in detail for the case of $N$ spin-$1/2$ particles. The discussed techniques can be readily implemented in current experiments with trapped ions in Paul traps and neutral atoms in optical lattices., Comment: 13 pages, 5 figures, 1 table

The detailed characterization of non-trivial coherence properties of composite quantum systems of increasing size is an indispensable prerequisite for scalable quantum computation, as well as for understanding of nonequilibrium many-body physics. Here we show how autocorrelation functions in an interacting system of phonons as well as the quantum discord between distinct degrees of freedoms can be extracted from a small controllable part of the system. As a benchmark, we show this in chains of up to 42 trapped ions, by tracing a single phonon excitation through interferometric measurements of only a single ion in the chain. We observe the spreading and partial refocusing of the excitation in the chain, even on a background of thermal excitations. We further show how this local observable reflects the dynamical evolution of quantum discord between the electronic state and the vibrational degrees of freedom of the probe ion., Comment: 22 pages, 4 figures

We provide a method to construct entanglement criteria for arbitrary multipartite systems of discrete or continuous variables and hybrid combinations of both. While any set of local operators generates a sufficient condition for entanglement of arbitrary quantum states, a suitable set leads to a necessary and sufficient criterion for pure states. The criteria are readily implementable with existing technology and reveal entanglement that remains undetected by the respective state-of-the-art methods for discrete and continuous variables., Comment: 6 pages, 2 figures

The quantum dynamics of a subset of interacting bosons in a subspace of fixed particle number is described in terms of symmetrized many-particle states. A suitable partial trace operation over the von Neumann equation of an $N$-particle system produces a hierarchical expansion for the subdynamics of $M\leq N$ particles. Truncating this hierarchy with a pure product state ansatz yields the general, nonlinear coherent mean-field equation of motion. In the special case of a contact interaction potential, this reproduces the Gross-Pitaevskii equation. To account for incoherent effects on top of the mean-field evolution, we discuss possible extensions towards a second-order perturbation theory that accounts for interaction-induced decoherence in form of a nonlinear Lindblad-type master equation., Comment: 33 pages

Quantum discord in a bipartite system can be dynamically revealed and quantified through purely local operations on one of the two subsystems. To achieve this, the local detection method harnesses the influence of initial correlations on the reduced dynamics of an interacting bipartite system. This article's aim is to provide an accessible introduction to this method and to review recent theoretical and experimental progress., Comment: 24 pages, 11 figures

We study the collective dephasing process of a system of non-interacting atomic qubits, immersed in a spatially uniform magnetic field of fluctuating intensity. The correlation properties of bipartite states are analysed based on a geometric representation of the state space. Particular emphasis is put on the dephasing-assisted generation of states with a high correlation rank, which can be related to discord-type correlations and allow for direct applications in quantum information theory. Finally we study the conditions that ensure the robustness of initial entanglement and discuss the phenomenon of time-invariant entanglement., Comment: 29 pages, 5 figures

We use an exact quantum phase model to study the dynamical generation of particle-entanglement in a bosonic Josephson junction composed by two coupled and interacting Bose-Einstein condensates. Using analytical arguments, we show that linear coupling can accelerate the creation of entanglement with respect to the well known one-axis twisting model where coupling is absent. Furthermore, with a numerical analysis of optimal control schemes, we identify the optimal parameters for the fast generation of metrologically useful entanglement on short time scales: the optimal evolution is generated for a specific ratio between the coupling and the interaction strength., Comment: new version, 12 pages, 10 figures

We study the excitation spectrum of a family of transverse-field spin chain models with variable interaction range and arbitrary spin $S$, which in the case of $S=1/2$ interpolates between the Lipkin-Meshkov-Glick and the Ising model. For any finite number $N$ of spins, a semiclassical energy manifold is derived in the large-$S$ limit employing bosonization methods, and its geometry is shown to determine not only the leading-order term but also the higher-order quantum fluctuations. Based on a multi-configurational mean-field ansatz, we obtain the semiclassical backbone of the quantum spectrum through the extremal points of a series of one-dimensional energy landscapes -- each one exhibiting a bifurcation when the external magnetic field drops below a threshold value. The obtained spectra become exact in the limit of vanishing or very strong external, transverse magnetic fields. Further analysis of the higher-order corrections in $1/\sqrt{2S}$ enables us to analytically study the dispersion relations of spin-wave excitations around the semiclassical energy levels. Within the same model, we are able to investigate quantum bifurcations, which occur in the semiclassical ($S\gg 1$) limit, and quantum phase transitions, which are observed in the thermodynamic ($N\rightarrow\infty$) limit., Comment: 20 pages, 13 figures

We devise a phase-coherent three-pulse protocol to probe the polariton dynamics in a trapped-ion quantum simulation. In contrast to conventional nonlinear signals, the presented scheme does not change the number of excitations in the system, allowing for the investigation of the dynamics within an $N$-excitation manifold. In the particular case of a filling factor one ($N$ excitations in an $N$-ion chain), the proposed interaction induces coherent transitions between a delocalized phonon superfluid and a localized atomic insulator phase. Numerical simulations of a two-ion chain demonstrate that the resulting two-dimensional spectra allow for the unambiguous identification of the distinct phases, and the two-dimensional lineshapes efficiently characterize the relevant decoherence mechanism.

We derive an analytic solution for the ensemble-averaged collective dephasing dynamics of $N$ noninteracting atoms in a fluctuating homogeneous external field. The obtained Kraus map is used to specify families of states whose entanglement properties are preserved at all times under arbitrary field orientations, even for states undergoing incoherent evolution. Our results apply to arbitrary spectral distributions of the field fluctuations., Comment: 7 pages (incl. Supplementary Materials), 3 figures