Atmospheric studies of habitability in the Gliese 581 system

The M-type star Gliese 581 is orbited by at least one terrestrial planet candidate in the habitable zone, i.e. GL 581 d. Orbital simulations have shown that additional planets inside the habitable zone of GL 581 would be dynamically stable. Recently, two further planet candidates have been claimed, one of them in the habitable zone. In view of the ongoing search for planets around M stars which is expected to result in numerous detections of potentially habitable Super-Earths, we take the GL 581 system as an example to investigate such planets. In contrast to previous studies of habitability in the GL 581 system, we use a consistent atmospheric model to assess surface conditions and habitability. Furthermore, we perform detailed atmospheric simulations for a much larger subset of potential planetary and atmospheric scenarios than previously considered. A 1D radiative-convective atmosphere model is used to calculate temperature and pressure profiles of model atmospheres, which we assumed to be composed of molecular nitrogen, water, and carbon dioxide. In these calculations, key parameters such as surface pressure and CO2 concentration as well as orbital distance and planetary mass are varied. Results imply that surface temperatures above freezing could be obtained, independent of the here considered atmospheric scenarios, at an orbital distance of 0.117 AU. For an orbital distance of 0.146 AU, CO2 concentrations as low as 10 times the present Earth's value are sufficient to warm the surface above the freezing point of water. At 0.175 AU, only scenarios with CO2 concentrations of 5% and 95% were found to be habitable. Hence, an additional Super-Earth planet in the GL 581 system in the previously determined dynamical stability range would be considered a potentially habitable planet.Comment: 5 pages, 4 figures, accepted in Astronomy&Astrophysic

Two quantum Simpson's paradoxes

The so-called Simpson's "paradox", or Yule-Simpson (YS) effect, occurs in classical statistics when the correlations that are present among different sets of samples are reversed if the sets are combined together, thus ignoring one or more lurking variables. Here we illustrate the occurrence of two analogue effects in quantum measurements. The first, which we term quantum-classical YS effect, may occur with quantum limited measurements and with lurking variables coming from the mixing of states, whereas the second, here referred to as quantum-quantum YS effect, may take place when coherent superpositions of quantum states are allowed. By analyzing quantum measurements on low dimensional systems (qubits and qutrits), we show that the two effects may occur independently, and that the quantum-quantum YS effect is more likely to occur than the corresponding quantum-classical one. We also found that there exist classes of superposition states for which the quantum-classical YS effect cannot occur for any measurement and, at the same time, the quantum-quantum YS effect takes place in a consistent fraction of the possible measurement settings. The occurrence of the effect in the presence of partial coherence is discussed as well as its possible implications for quantum hypothesis testing.Comment: published versio

Quantum estimation via minimum Kullback entropy principle

We address quantum estimation in situations where one has at disposal data from the measurement of an incomplete set of observables and some a priori information on the state itself. By expressing the a priori information in terms of a bias toward a given state the problem may be faced by minimizing the quantum relative entropy (Kullback entropy) with the constraint of reproducing the data. We exploit the resulting minimum Kullback entropy principle for the estimation of a quantum state from the measurement of a single observable, either from the sole mean value or from the complete probability distribution, and apply it as a tool for the estimation of weak Hamiltonian processes. Qubit and harmonic oscillator systems are analyzed in some details.Comment: 7 pages, slightly revised version, no figure

High efficiency tomographic reconstruction of quantum states by quantum nondemolition measurements

We propose a high efficiency tomographic scheme to reconstruct an unknown quantum state of the qubits by using a series of quantum nondemolition (QND) measurements. The proposed QND measurements of the qubits are implemented by probing the the stationary transmissions of the dispersively-coupled resonator. It is shown that only one kind of QND measurements is sufficient to determine all the diagonal elements of the density matrix of the detected quantum state. The remaining non-diagonal elements of the density matrix can be determined by other spectral measurements by beforehand transferring them to the diagonal locations using a series of unitary operations. Compared with the pervious tomographic reconstructions based on the usual destructively projective (DP) measurements (wherein one kind of such measurements could only determine one diagonal element of the density matrix), the present approach exhibits significantly high efficiency for N-qubit (N > 1). Specifically, our generic proposal is demonstrated by the experimental circuit-quantumelectrodynamics (circuit-QED) systems with a few Josephson charge qubits.Comment: 9pages,4figure

Information criteria for efficient quantum state estimation

Recently several more efficient versions of quantum state tomography have been proposed, with the purpose of making tomography feasible even for many-qubit states. The number of state parameters to be estimated is reduced by tentatively introducing certain simplifying assumptions on the form of the quantum state, and subsequently using the data to rigorously verify these assumptions. The simplifying assumptions considered so far were (i) the state can be well approximated to be of low rank, or (ii) the state can be well approximated as a matrix product state. We add one more method in that same spirit: we allow in principle any model for the state, using any (small) number of parameters (which can, e.g., be chosen to have a clear physical meaning), and the data are used to verify the model. The proof that this method is valid cannot be as strict as in above-mentioned cases, but is based on well-established statistical methods that go under the name of "information criteria." We exploit here, in particular, the Akaike Information Criterion (AIC). We illustrate the method by simulating experiments on (noisy) Dicke states

Entanglement and visibility at the output of a Mach-Zehnder interferometer

We study the entanglement between the two beams exiting a Mach-Zehnder interferometer fed by a couple of squeezed-coherent states with arbitrary squeezing parameter. The quantum correlations at the output are function of the internal phase-shift of the interferometer, with the output state ranging from a totally disentangled state to a state whose degree of entanglement is an increasing function of the input squeezing parameter. A couple of squeezed vacuum at the input leads to maximum entangled state at the output. The fringes visibilities resulting from measuring the coincidence counting rate or the squared difference photocurrent are evaluated and compared each other. Homodyne-like detection turns out to be preferable in almost all situations, with the exception of the very low signals regime.Comment: 6 figs, accepted for publication on PRA, see also http://enterprise.pv.infn.it/~pari

Phase estimation for thermal Gaussian states

We give the optimal bounds on the phase-estimation precision for mixed Gaussian states in the single-copy and many-copy regimes. Specifically, we focus on displaced thermal and squeezed thermal states. We find that while for displaced thermal states an increase in temperature reduces the estimation fidelity, for squeezed thermal states a larger temperature can enhance the estimation fidelity. The many-copy optimal bounds are compared with the minimum variance achieved by three important single-shot measurement strategies. We show that the single-copy canonical phase measurement does not always attain the optimal bounds in the many-copy scenario. Adaptive homodyning schemes do attain the bounds for displaced thermal states, but for squeezed states they yield fidelities that are insensitive to temperature variations and are, therefore, sub-optimal. Finally, we find that heterodyne measurements perform very poorly for pure states but can attain the optimal bounds for sufficiently mixed states. We apply our results to investigate the influence of losses in an optical metrology experiment. In the presence of losses squeezed states cease to provide Heisenberg limited precision and their performance is close to that of coherent states with the same mean photon number.Comment: typos correcte

Optimal estimation of joint parameters in phase space

We address the joint estimation of the two defining parameters of a displacement operation in phase space. In a measurement scheme based on a Gaussian probe field and two homodyne detectors, it is shown that both conjugated parameters can be measured below the standard quantum limit when the probe field is entangled. We derive the most informative Cram\'er-Rao bound, providing the theoretical benchmark on the estimation and observe that our scheme is nearly optimal for a wide parameter range characterizing the probe field. We discuss the role of the entanglement as well as the relation between our measurement strategy and the generalized uncertainty relations.Comment: 8 pages, 3 figures; v2: references added and sections added to the supplemental material; v3: minor changes (published version

Automatic Photo Adjustment Using Deep Neural Networks

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The extrasolar planet Gliese 581 d: a potentially habitable planet? (Corrigendum to arXiv:1009.5814)

We report here that the equation for H2O Rayleigh scattering was incorrectly stated in the original paper [arXiv:1009.5814]. Instead of a quadratic dependence on refractivity r, we accidentally quoted an r^4 dependence. Since the correct form of the equation was implemented into the model, scientific results are not affected.Comment: accepted to Astronomy&Astrophysic