We discuss the problem of separation of total correlations in a given quantum state into entanglement, dissonance, and classical correlations using the concept of relative entropy as a distance measure of correlations. This allows us to put all correlations on an equal footing. Entanglement and dissonance, whose definition is introduced here, jointly belong to what is known as quantum discord. Our methods are completely applicable for multipartite systems of arbitrary dimensions. We investigate additivity relations between different correlations and show that dissonance may be present in pure multipartite states.Introduction.-Quantum systems are correlated in ways inaccessible to classical objects. A distinctive quantum feature of correlations is quantum entanglement [1][2][3]. Entangled states are nonclassical as they cannot be prepared with the help of local operations and classical communication (LOCC) [4]. However, it is not the only aspect of nonclassicality of correlations due to the nature of operations allowed in the framework of LOCC. To illustrate this, one can compare a classical bit with a quantum bit; in the case of full knowledge about a classical bit, it is completely described by one of two locally distinguishable states, and the only allowed operations on the classical bit are to keep its value or flip it. To the contrary, quantum operations can prepare quantum states that are indistinguishable for a given measurement. Such operations and classical communication can lead to separable states (those which can be prepared via LOCC) which are mixtures of locally indistinguishable states. These states are nonclassical in the sense that they cannot be prepared using classical operations on classical bits.Recent measures of nonclassical correlations are motivated by different notions of classicality and operational means to quantify nonclassicality [5][6][7][8][9]. Quantum discord has received much attention in studies involving thermodynamics and correlations [10][11][12], positivity of dynamics [13,14], quantum computation [15][16][17][18], broadcasting of quantum states [19,20], dynamics of discord [21][22][23], and volume of discord [24,25]. Most of these works are limited to studies of bipartite correlations only as the concept of discord, which relies on the definition of mutual information, is not defined for multipartite systems. In some of the studies, it is also desirable to compare various notions of quantum correlations. It is well known that the different measures of quantum correlation are not identical and conceptually different. For example, the discord does not coincide with entanglement and a direct comparison of two notions is rather meaningless. Therefore, an unified classification of correlations is in demand.In this Letter, we resolve these two issues by introducing a measure for classical and nonclassical correlations

Earth system models are complex and represent a large number of processes, resulting in a persistent spread across climate projections for a given future scenario. Owing to different model performances against observations and the lack of independence among models, there is now evidence that giving equal weight to each available model projection is suboptimal. This Perspective discusses newly developed tools that facilitate a more rapid and comprehensive evaluation of model simulations with observations, process-based emergent constraints that are a promising way to focus evaluation on the observations most relevant to climate projections, and advanced methods for model weighting. These approaches are needed to distil the most credible information on regional climate changes, impacts, and risks for stakeholders and policy-makers.

Equilibrium climate sensitivity (ECS) remains one of the most important unknowns in climate change science. ECS is defined as the global mean warming that would occur if the atmospheric carbon dioxide (CO) concentration were instantly doubled and the climate were then brought to equilibrium with that new level of CO. Despite its rather idealized definition, ECS has continuing relevance for international climate change agreements, which are often framed in terms of stabilization of global warming relative to the pre-industrial climate. However, the 'likely' range of ECS as stated by the Intergovernmental Panel on Climate Change (IPCC) has remained at 1.5-4.5 degrees Celsius for more than 25 years. The possibility of a value of ECS towards the upper end of this range reduces the feasibility of avoiding 2 degrees Celsius of global warming, as required by the Paris Agreement. Here we present a new emergent constraint on ECS that yields a central estimate of 2.8 degrees Celsius with 66 per cent confidence limits (equivalent to the IPCC 'likely' range) of 2.2-3.4 degrees Celsius. Our approach is to focus on the variability of temperature about long-term historical warming, rather than on the warming trend itself. We use an ensemble of climate models to define an emergent relationship between ECS and a theoretically informed metric of global temperature variability. This metric of variability can also be calculated from observational records of global warming, which enables tighter constraints to be placed on ECS, reducing the probability of ECS being less than 1.5 degrees Celsius to less than 3 per cent, and the probability of ECS exceeding 4.5 degrees Celsius to less than 1 per cent.

We analyze the effects of quantum correlations, such as entanglement and discord, on the efficiency of phase estimation by studying four quantum circuits that can be readily implemented using NMR techniques. These circuits define a standard strategy of repeated single-qubit measurements, a classical strategy where only classical correlations are allowed, and two quantum strategies where nonclassical correlations are allowed. In addition to counting space (number of qubits) and time (number of gates) requirements, we introduce mixedness as a key constraint of the experiment. We compare the efficiency of the four strategies as a function of the mixedness parameter. We find that the quantum strategy gives ffiffiffiffi N p enhancement over the standard strategy for the same amount of mixedness. This result applies even for highly mixed states that have nonclassical correlations but no entanglement.

Abstract. Climate sensitivity to CO2 remains the key uncertainty in projections of future climate change. Transient climate response (TCR) is the metric of temperature sensitivity that is most relevant to warming in the next few decades and contributes the biggest uncertainty to estimates of the carbon budgets consistent with the Paris targets. Equilibrium climate sensitivity (ECS) is vital for understanding longer-term climate change and stabilisation targets. In the IPCC 5th Assessment Report (AR5), the stated “likely” ranges (16 %–84 % confidence) of TCR (1.0–2.5 K) and ECS (1.5–4.5 K) were broadly consistent with the ensemble of CMIP5 Earth system models (ESMs) available at the time. However, many of the latest CMIP6 ESMs have larger climate sensitivities, with 5 of 34 models having TCR values above 2.5 K and an ensemble mean TCR of 2.0±0.4 K. Even starker, 12 of 34 models have an ECS value above 4.5 K. On the face of it, these latest ESM results suggest that the IPCC likely ranges may need revising upwards, which would cast further doubt on the feasibility of the Paris targets. Here we show that rather than increasing the uncertainty in climate sensitivity, the CMIP6 models help to constrain the likely range of TCR to 1.3–2.1 K, with a central estimate of 1.68 K. We reach this conclusion through an emergent constraint approach which relates the value of TCR linearly to the global warming from 1975 onwards. This is a period when the signal-to-noise ratio of the net radiative forcing increases strongly, so that uncertainties in aerosol forcing become progressively less problematic. We find a consistent emergent constraint on TCR when we apply the same method to CMIP5 models. Our constraints on TCR are in good agreement with other recent studies which analysed CMIP ensembles. The relationship between ECS and the post-1975 warming trend is less direct and also non-linear. However, we are able to derive a likely range of ECS of 1.9–3.4 K from the CMIP6 models by assuming an underlying emergent relationship based on a two-box energy balance model. Despite some methodological differences; this is consistent with a previously published ECS constraint derived from warming trends in CMIP5 models to 2005. Our results seem to be part of a growing consensus amongst studies that have applied the emergent constraint approach to different model ensembles and to different aspects of the record of global warming.

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Effects of atmospheric dynamics and ocean resolution on bi-stability of the thermohaline circulation examined using the Grid ENabled Integrated Earth system modelling (GENIE) framework AbstractWe have used the Grid ENabled Integrated Earth system modelling (GENIE) framework to undertake a systematic search for bi-stability of the ocean thermohaline circulation (THC) for different surface grids and resolutions of 3-D ocean (GOLDSTEIN) under a 3-D dynamical atmosphere model (IGCM). A total of 407,000 years were simulated over a three month period using Grid computing. We find bi-stability of the THC despite significant, quasi-periodic variability in its strength driven by variability in the dynamical atmosphere. The position and width of the hysteresis loop depends on the choice of surface grid (longitude-latitude or equal area), but is less sensitive to changes in ocean resolution. For the same ocean resolution, the region of bi-stability is broader with the IGCM than with a simple energy-moisture balance atmosphere model (EMBM).