Structure of multiphoton quantum optics. II. Bipartite systems, physical processes, and heterodyne squeezed states

Extending the scheme developed for a single mode of the electromagnetic field in the preceding paper ``Structure of multiphoton quantum optics. I. Canonical formalism and homodyne squeezed states'', we introduce two-mode nonlinear canonical transformations depending on two heterodyne mixing angles. They are defined in terms of hermitian nonlinear functions that realize heterodyne superpositions of conjugate quadratures of bipartite systems. The canonical transformations diagonalize a class of Hamiltonians describing non degenerate and degenerate multiphoton processes. We determine the coherent states associated to the canonical transformations, which generalize the non degenerate two--photon squeezed states. Such heterodyne multiphoton squeezed are defined as the simultaneous eigenstates of the transformed, coupled annihilation operators. They are generated by nonlinear unitary evolutions acting on two-mode squeezed states. They are non Gaussian, highly non classical, entangled states. For a quadratic nonlinearity the heterodyne multiphoton squeezed states define two--mode cubic phase states. The statistical properties of these states can be widely adjusted by tuning the heterodyne mixing angles, the phases of the nonlinear couplings, as well as the strength of the nonlinearity. For quadratic nonlinearity, we study the higher-order contributions to the susceptibility in nonlinear media and we suggest possible experimental realizations of multiphoton conversion processes generating the cubic-phase heterodyne squeezed states.Comment: 16 pages, 23 figure

Optimal estimation of losses at the ultimate quantum limit with non-Gaussian states

We address the estimation of the loss parameter of a bosonic channel probed by arbitrary signals. Unlike the optimal Gaussian probes, which can attain the ultimate bound on precision asymptotically either for very small or very large losses, we prove that Fock states at any fixed photon number saturate the bound unconditionally for any value of the loss. In the relevant regime of low-energy probes, we demonstrate that superpositions of the first low-lying Fock states yield an absolute improvement over any Gaussian probe. Such few-photon states can be recast quite generally as truncations of de-Gaussified photon-subtracted states.Comment: 4 pages, 3 figure

Hierarchies of Geometric Entanglement

We introduce a class of generalized geometric measures of entanglement. For pure quantum states of $N$ elementary subsystems, they are defined as the distances from the sets of $K$-separable states ($K=2,...,N$). The entire set of generalized geometric measures provides a quantification and hierarchical ordering of the different bipartite and multipartite components of the global geometric entanglement, and allows to discriminate among the different contributions. The extended measures are applied to the study of entanglement in different classes of $N$-qubit pure states. These classes include $W$ and $GHZ$ states, and their symmetric superpositions; symmetric multi-magnon states; cluster states; and, finally, asymmetric generalized $W$-like superposition states. We discuss in detail a general method for the explicit evaluation of the multipartite components of geometric entanglement, and we show that the entire set of geometric measures establishes an ordering among the different types of bipartite and multipartite entanglement. In particular, it determines a consistent hierarchy between $GHZ$ and $W$ states, clarifying the original result of Wei and Goldbart that $W$ states possess a larger global entanglement than $GHZ$ states. Furthermore, we show that all multipartite components of geometric entanglement in symmetric states obey a property of self-similarity and scale invariance with the total number of qubits and the number of qubits per party.Comment: 16 pages, 7 figures. Final version, to appear in Phys. Rev.

Quantum characterization of bipartite Gaussian states

Gaussian bipartite states are basic tools for the realization of quantum information protocols with continuous variables. Their complete characterization is obtained by the reconstruction of the corresponding covariance matrix. Here we describe in details and experimentally demonstrate a robust and reliable method to fully characterize bipartite optical Gaussian states by means of a single homodyne detector. We have successfully applied our method to the bipartite states generated by a sub-threshold type-II optical parametric oscillator which produces a pair of thermal cross-polarized entangled CW frequency degenerate beams. The method provide a reliable reconstruction of the covariance matrix and allows to retrieve all the physical information about the state under investigation. These includes observable quantities, as energy and squeezing, as well as non observable ones as purity, entropy and entanglement. Our procedure also includes advanced tests for Gaussianity of the state and, overall, represents a powerful tool to study bipartite Gaussian state from the generation stage to the detection one

Multipartite entangled states in particle mixing

In the physics of flavor mixing, the flavor states are given by superpositions of mass eigenstates. By using the occupation number to define a multiqubit space, the flavor states can be interpreted as multipartite mode-entangled states. By exploiting a suitable global measure of entanglement, based on the entropies related to all possible bipartitions of the system, we analyze the correlation properties of such states in the instances of three- and four-flavor mixing. Depending on the mixing parameters, and, in particular, on the values taken by the free phases, responsible for the CP-violation, entanglement concentrates in preferred bipartitions. We quantify in detail the amount and the distribution of entanglement in the physically relevant cases of flavor mixing in quark and neutrino systems. By using the wave packet description for localized particles, we use the global measure of entanglement, suitably adapted for the instance of multipartite mixed states, to analyze the decoherence induced by the free evolution dynamics on the quantum correlations of stationary neutrino beams. We define a decoherence length as the distance associated with the vanishing of the coherent interference effects among massive neutrino states. We investigate the role of the CP-violating phase in the decoherence process.Comment: 18 pages, 7 figure

Developmental perspectives on Europe

The crisis of 2008–2009 has ended, stockmarkets skyrocketed in 2012–2013, while growth of the real sector remained sluggish in Europe. This article attempts to explain the latter puzzle. Analyzing long term factors, the costs of short-termism in crisis management become obvious. The limitations of EU as a growth engine are highlighted

A study of the efficiency of the class of WW-states as a quantum channel

Recently, a new class of $W$-states has been defined by Agarwal and Pati \cite{agarwal} and it has been shown that they can be used as a quantum channel for teleportation and superdense coding. In this work, we identify those three-qubit states from the set of the new class of $W$-states which are most efficient or suitable for quantum teleportation. We show that with some probability $|W_1>=(1/2)(|100>+|010>+\sqrt{2}|001>)$ is best suited for teleportation channel in the sense that it does not depend on the input state.Comment: 7 pages, Late

Prospect theory and tax evasion: a reconsideration of the Yitzhaki puzzle

The standard expected utility (EUT) model of tax evasion predicts that evasion is decreasing in the marginal tax rate (the Yitzhaki puzzle). Recent literature shows cases in which incorporating prospect theory (PT) does and does not overturn the Puzzle. In a general environment that nests both PT and EUT preferences, we provide a detailed study of how the elements of PT affect the Puzzle. PT does not always reverse the Puzzle, hence we give and interpret conditions for when it does and does not. When allowing for stigma and/or variable audit probability, PT reverses the Puzzle in the same way and with the same limitations as does EUT, if equally augmented

Exchange of nutrients and oxygen across the sediment-water interface below a Sparus aurata marine fish farm in the north-western Mediterranean Sea

Purpose: This study analyzes the effects of aquaculture activities in open seawater in the north-western coastal waters of the Mediterranean Sea. It is the first of its kind to be based on benthic flux data gathered in situ below fish farms for this particular area. Materials and methods: Samples were collected on four sampling campaigns over a 1-year cycle under a Sparus aurata fish farm facility where benthic fluxes were measured in situ using light and dark benthic chambers. Bottom water and sediment samples were also collected. Data were compared to those for a nearby control station. Results and discussion: Significant differences were found (ANOVA, p < 0. 05) between concentrations of organic matter (OM), total phosphorus and redox potentials in sediments located under the cages and those of the control station. The consumption of dissolved oxygen (DO) by sediment and positive ammonium (NH4 +) fluxes was stimulated by OM content, with correlations of r = -0. 60 (p < 0. 01) and r = 0. 70 (p < 0. 01), respectively. The OM content of sediments was found to be consistently higher under the cages than at the control station, with the highest value (1. 8 ± 0. 7 %) under the cages observed during the early summer; values of DO and NH4 + fluxes were -64 ± 17 and 12. 7 ± 1. 0 mmol m-2 day-1, respectively. PO4 3- fluxes were consistently higher in the fish farm sediments (between 0. 58 and 0. 98 mmol m-2 day-1) than those observed at the control station. Nitrate (NO3 -) fluxes were found to be consistently negative due to denitrification occurring in the sediments and were related to the concentration of NO3 - in bottom waters (r = 0. 92, p < 0. 01). Si fluxes were shown to be associated with water temperature (r = 0. 59, p < 0. 05). Conclusions: The results imply that sediments located below cages accumulate organic matter originating from aquaculture activities, especially during summer months when this activity increases. Sediments undergo biogeochemical changes that mainly affect fluxes of DO, NH4 + and soluble reactive phosphorus, although these do not seem to have a significant impact on the quality of the water column due to the hydrodynamic characteristics of the area. © 2012 Springer-Verlag.We would like to thank the Caja del Mediterraneo for a predoctoral fellowship fund for this research and Antonio Asuncion Acuigroup Maremar manager for the facilities and support in conducting the study. The translation of this paper was funded by the Universidad Politecnica de Valencia, Spain. We are grateful for the valuable comments of the anonymous reviewers on previous versions of the manuscript.Morata Higón, T.; Sospedra, J.; Falco Giaccaglia, SL.; Rodilla Alama, M. (2012). Exchange of nutrients and oxygen across the sediment-water interface below a Sparus aurata marine fish farm in the north-western Mediterranean Sea. Journal of Soils and Sediments. 12(10):1623-1632. doi:10.1007/s11368-012-0581-2S162316321210APHA, AWWA, and WEF (2005) Standard methods for the examination of water wastewater, 21st edn. American Public Health Association, WashingtonAksu M, Kocatas A (2007) Environmental effects of the three fish farms in Izmir Bay (Aegean Sea-Turkey) on water column and sediment. Rapport du 38e Congrés de la Commission Internationale Pour L’exploration Scientifique de la Mer Méditerranée 38, 414Aminot A, Chaussepied M (1983) Manuel des analyses chimiques en milieu marin. Centre National pour l’Explotation des Oceans, BrestArocena R, Conde D (1999) Sedimento. Métodos en ecología de aguas continentales. Universidad de la República, Montevideo, pp 40–52Asociación Empresarial de Productores de Cultivos Marinas (APROMAR) (2010) La Acuicultura Marina de Peces en España, pp. 69Baumgarten MGZ, Rocha JM, Niencheski LFH (1996) Manual de análises em oceanografia química, Rio GrandeBelias C, Dassenakis M, Scoullos M (2007) Study of the N, P and Si fluxes between fish farm sediment and seawater. Results of simulation experiments employing a benthic chamber under various redox conditions. Mar Chem 103:266–275Berelson WM, McManus J, Coale KH, Johnson KS, Burdige D, Kilgore T, Colodner D, Chavez F, Kudela R, Boucher J (2003) A time series of benthic flux measurements from Monterey Bay, CA. Cont Shelf Res 23:457–481Black KD, McDougall N (2002) Hydrography of four Mediterranean marine cage sites. J Appl Ichthyol 18:129–133Borja A, Rodríguez JG, Black K, Bodoy A, Emblow C, Fernandes TF, Forte J, Karakassis I, Muxika I, Nickell TD, Papageorgiou N, Pranovi F, Sevastou K, Tomassetti P, Angel D (2009) Assessing the suitability of a range of benthic indices in the evaluation of environmental impact of fin and shellfish aquaculture located in sites across Europe. Aquaculture 293:231–240Cermelj B, Ogrinc N, Faganeli J (2001) Anoxic mineralization of biogenic debris in near-shore marine sediments (Gulf of Trieste, northern Adriatic). Sci Total Environ 266:143–152Dell’Anno A, Mei ML, Pusceddu A, Danovaro R (2002) Assessing the trophic state and eutrophication of coastal marine systems: a new approach based on the biochemical composition of sediment organic matter. Mar Pollut Bull 44:611–622Dosdat A (2001) Environmental impact of aquaculture in the Mediterranean: nutritional and feeding aspects. Environmental impact assessment of Mediterranean aquaculture farms. Cah Options Méditerr CIHEAM-FAO 55:23–36Ferrón S, Ortega T, Forja JM (2009) Benthic fluxes in a tidal salt marsh creek by fish farm activities: Río San Pedro (Bay of Cádiz, SW Spain). Mar Chem 113:50–62Freitas U, Niencheski LFH, Zarzur S, Manzolli RP, Vieira JPP, Rosa LC (2008) Influência de um cultivo de camaraô sobre o metabolismo béntico e a qualidade da agua. Rev Bras Eng Agríc Ambient 12:293–301Hall POJ, Holby O, Kollberg S, Samuelsson MO (1992) Chemical fluxes and mass balances in a marine fish cage farm: IV. Nitrogen. Mar Ecol Prog Ser 89:81–91Hargrave B (2005) Environmental effects of marine finfish aquaculture. The handbook of environmental. chemistry, vol. 5. Part M. Springer, BerlinHargrave BT, Phillips GA, Doucette LI, White MJ, Milligan TG, Wildish DJ, Cranston RE (1997) Assessing benthic impacts of organic enrichment from marine aquaculture. Water Air Soil Pollut 99:641–650Heilskov AC, Holmer M (2001) Effects of benthic fauna on organic matter mineralization in fish-farm sediments: importance of size and abundance. ICES J Mar Sci 58:427–434Herbert RA (1999) Nitrogen cycling in coastal marine ecosystems. FEMS Microbiol Rev 23:563–590Holby O, Hall POJ (1991) Chemical fluxes and mass balances in a marine fish cage farm. 11. Phosphorus. Mar Ecol Prog Ser 70:263–272Holby O, Hall POJ (1994) Chemical fluxes and mass balances in a marine fish cage farm. III. Silicon. Aquaculture 120:305–318Jackson C, Preston N, Thompson PJ (2004) Intake and discharge nutrient loads at three intensive shrimp farms. Aquacult Res 35:1053–1061Karakassis I, Tsapakis M, Hatziyanni E (1998) Seasonal variability in sediment profiles beneath fish farm cages in the Mediterranean. Mar Ecol Prog Ser 162:243–252Kaymakci A, Aksu M, Egemen O (2010) Impacts of the fish farms on the water column nutrient concentrations and accumulation of heavy metals in the sediments in the eastern Aegean Sea (Turkey). Environ Monit Assess 162:439–451Lorenti M, De Falco G (2004) Measurements and characterization of abiotic variables. In: Gambi MC, Diappiano M (eds) Mediterranean marine benthos: a manual of methods for its sampling and study. Societa Italiana di Biologia Marina, Genova, pp 1–37Maldonado M, Carmona MC, Echeverría Y, Riesgo A (2005) The environmental impact of Mediterranean cage fish farms at semi-exposed locations: does it need a re-assessment? Helgol Mar Res 59:121–135Mantzavrakos E, Kornaros M, Lyberatos G, Kaspiris P (2007) Impacts of a marine fish farm in Argolikos Gulf (Greece) on the water column and the sediment. Desalination 210:110–124Mazzola A, Mirto S, La Rosa T, Fabiano M, Danovaro R (2000) Fish-farming effects on benthic community structure in coastal sediments: analysis of meiofaunal recovery. ICES J Mar Sci 57:1454–1461Molina L, Vergara JM (2005) Impacto ambiental de jaulas flotantes: estado actual de conocimientos y conclusiones prácticas. Bol Inst Esp Oceanogr 21:75–81Morán XAG, Estrada M (2005) Winter pelagic photosynthesis in the NW Mediterranean Deep-Sea. Research I 52:1806–1822Neofitou N, Klaoudatos S (2008) Effect of fish farming on the water column nutrient concentration in a semi-enclosed gulf of the Eastern Mediterranean. Aquac Res 39:482–490Niencheski LF, Jahnke RA (2002) Benthic respiration and inorganic nutrient fluxes in the estuarine región of Patos Lagoon (Brazil). Aquat Geochem 8:135–152Nizzoli D, Bartoli M, Viaroli P (2007) Oxygen and ammonium dynamics during a farming cycle of the bivalve Tapes philippinarum. Hydrobiologia 587:25–36Pergent-Martini C, Boudouresque CF, Pasqualini V, Pergent G (2006) Impact of fish farming facilities on Posidonia oceanica meadows: a review. Mar Ecol 27:310–319Pitta P, Karakassis I, Tsapakis M, Zivanovic S (1999) Natural versus mariculture induced variability in nutrients and plankton in the Eastern Mediterranean. Hydrobiologia 391:181–194Redfield AC, Ketchum BH, Richards FA (1963) The influence of organisms on the composition of seawater. In: Hill MN (ed) The sea, vol 2. Interscience, New YorkRiise JC, Roos N (1997) Benthic metabolism and the effects of bioturbation in a fertilized polyculture fish pond in northeast Thailand. Aquaculture 150:45–62Rodríguez J (1999) Ecología. Ed. Pirámide. pp 411Sakamaki T, Nishimura O, Sudo R (2006) Tidal time-scale variation in nutrient flux across the sediment-water interface of an estuarine tidal flat. Estuar Coast Shelf Sci 67:653–663Sarà G, Scilipoti D, Milazzo M, Modica A (2006) Use of stable isotopes to investigate dispersal of waste from fish farms as a function of hydrodynamics. Mar Ecol Prog Ser 313:261–270Shepard FP (1954) Nomenclature based on sand-silt-clay relations. J Sediment Petrol 24:151–158Siokou-Frangou I, Christaki U, Mazzocchi MG, Montresor M, Ribera d’Alcalá M, Vaqué D, Zingone A (2010) Plankton in the open Mediterranean Sea: a review. BG 7:1543–1586Warnken KW, Gill GA, Lehman R, Dellapenna T, Allison MA (2002) The effects of shrimp trawling on sediment oxygen demand and the release of trace metals and nutrients from estuarine sediments. Estuar Coast Shelf Sci 57:25–42Yucel-Gier G, Kucuksezgin F, Kocak F (2007) Effects of fish farming on nutrients and benthic community structure in the Eastern Aegean (Turkey). Aquac Res 38:256–26