Geometry of unital quantum maps and locally maximally mixed bipartite states

In this thesis, we consider the geometry of the set of unital quantum maps and the geometry of the set of bipartite states with maximally mixed marginals. By the map-state duality, these two sets are isomorphic and can be considered by using the same mathematical formalism. When considering the geometry of unital quantum maps we encounter one crucial difference between two-dimensional systems and systems of higher dimensions. Unital qubit maps can be decomposed in terms of unitary maps. However, non-unitary maps need to be considered to decompose other unital qudit maps. To consider the geometry of unital quantum maps in higher dimensions, we construct a novel family of maps that includes both unitary and non-unitary unital quantum maps. For this family, we derive a criterion determining whether a given map of the family corresponds to an extreme point of the set of unital quantum maps. By applying the Choi-Jamiolkowski isomorphism over the family of maps, we consider the geometry of the set of locally maximally mixed bipartite states. In particular, we consider the problem of entanglement classification for the elements of this family of bipartite states. To do this, we find a set of invariants determining local unitary classes for our family. We also consider this family of bipartite states for qutrit systems. Remarkably, in this scenario, the chosen set of invariants can be used for the entanglement classification of the states of the family. For qutrit states, we consider the solutions of the equations giving unital quantum maps and locally maximally mixed bipartite states for the families previously considered. To do this, we construct an algorithm based on numerical methods to solve these equations. We also provide a graphical representation of the solutions given by the algorithm. Finally, we consider a constraint in the parameters of the equations allowing us to obtain solutions with analytical methods

Mid-infrared imaging- and spectro-polarimetric subarcsecond observations of NGC 1068

We present sub-arcsecond 7.5$-$13 $\mu$m imaging- and spectro-polarimetric observations of NGC 1068 using CanariCam on the 10.4-m Gran Telescopio CANARIAS. At all wavelengths, we find: (1) A 90 $\times$ 60 pc extended polarized feature in the northern ionization cone, with a uniform $\sim$44$^{\circ}$ polarization angle. Its polarization arises from dust and gas emission in the ionization cone, heated by the active nucleus and jet, and further extinguished by aligned dust grains in the host galaxy. The polarization spectrum of the jet-molecular cloud interaction at $\sim$24 pc from the core is highly polarized, and does not show a silicate feature, suggesting that the dust grains are different from those in the interstellar medium. (2) A southern polarized feature at $\sim$9.6 pc from the core. Its polarization arises from a dust emission component extinguished by a large concentration of dust in the galaxy disc. We cannot distinguish between dust emission from magnetically aligned dust grains directly heated by the jet close to the core, and aligned dust grains in the dusty obscuring material surrounding the central engine. Silicate-like grains reproduce the polarized dust emission in this feature, suggesting different dust compositions in both ionization cones. (3) An upper limit of polarization degree of 0.3 per cent in the core. Based on our polarization model, the expected polarization of the obscuring dusty material is $\lesssim$0.1 per cent in the 8$-$13 $\mu$m wavelength range. This low polarization may be arising from the passage of radiation through aligned dust grains in the shielded edges of the clumps.Comment: 17 pages, 10 figures, accepted for publication at MNRA

Starburst radio galaxies: general properties, evolutionary histories and triggering

In this paper we discuss the results of a programme of spectral synthesis modelling of a sample of starburst radio galaxies in the context of scenarios for the triggering of the activity and the evolution of the host galaxies. The starburst radio galaxies -- comprising ~15 - 25% of all powerful extragalactic radio sources -- frequently show disturbed morphologies at optical wavelengths, and unusual radio structures, although their stellar masses are typical of radio galaxies as a class. In terms of the characteristic ages of their young stellar populations (YSP), the objects can be divided into two groups: those with YSP ages t_ysp < 0.1 Gyr, in which the radio source has been triggered quasi-simultaneously with the main starburst episode, and those with older YSP in which the radio source has been triggered or re-triggered a significant period after the starburst episode. Combining the information on the YSP with that on the optical morphologies of the host galaxies, we deduce that the majority of the starburst radio galaxies have been triggered in galaxy mergers in which at least one of the galaxies is gas rich. However, the triggering (or re-triggering) of the radio jets can occur immediately before, around, or a significant period after the final coalescence of the merging nuclei, reflecting the complex gas infall histories of the merger events. Overall, our results provide further evidence that powerful radio jet activity can be triggered via a variety of mechanisms, including different evolutionary stages of major galaxy mergers; clearly radio-loud AGN activity is not solely associated with a particular stage of a unique type of gas accretion event.Comment: 16 pages, 3 Figures, accepted for publication in MNRA

Controllable direction of liquid jets generated by thermocavitation within a droplet.

A high-velocity fluid stream ejected from an orifice or nozzle is a common mechanism to produce liquid jets in inkjet printers or to produce sprays among other applications. In the present research, we show the generation of liquid jets of controllable direction produced within a sessile water droplet by thermocavitation. The jets are driven by an acoustic shock wave emitted by the collapse of a hemispherical vapor bubble at the liquid-solid/substrate interface. The generated shock wave is reflected at the liquid-air interface due to acoustic impedance mismatch generating multiple reflections inside the droplet. During each reflection, a force is exerted on the interface driving the jets. Depending on the position of the generation of the bubble within the droplet, the mechanical energy of the shock wave is focused on different regions at the liquid-air interface, ejecting cylindrical liquid jets at different angles. The ejected jet angle dependence is explained by a simple ray tracing model of the propagation of the acoustic shock wave inside the droplet

Synthesis of noble metal-decorated NH2-MIL-125 titanium MOF for the photocatalytic degradation of acetaminophen under solar irradiation

This work reports the solvothermal synthesis of a titanium-based metal organic framework (NH2-MIL-125(Ti)) and the further deposition of palladium, platinum and silver nanoparticles on its framework, with the aim to obtain visible light-driven photocatalysts. The structure of the NH2-MIL-125 was not affected by the incorporation of the metal nanoparticles, while the textural properties changed depending on the metal used. All M/NH2-MIL-125 (M = Pd, Pt, Ag) synthesized materials showed enhanced light absorption in the visible region due to the effect of the metal nanoparticles, which were mainly in reduced state as confirmed by XPS analyses. The metal nanoparticles were between 1.8 and 3.8 nm in size depending of the metal. They were responsible for the reduction in the recombination process, as suggested by photoluminescence measurements. The photocatalytic performance of M/NH2-MIL-125 was tested for the degradation of acetaminophen (ACE) under simulated solar irradiation. Pt/NH2-MIL-125 achieved the highest conversion rate (rate constant of 0.0165 min−1), with complete conversion of the contaminant in less than three hours. Scavengers studies confirmed that O.-2[rad]− radicals play a main role in the degradation process, followed by .OH radicals. The catalytic stability of Pt/NH2-MIL-125 was confirmed upon three successive reaction cycles. Different water matrices were tested to understand the effect of common inorganic ions, being the presence of bicarbonates the most detrimental to the performance of the photocatalytic processThis research was funded by the State Research Agency (PID2019-106186RB-I00/AEI/10.13039/501100011033). V. Muelas-Ramos thanks to MCIU for BES-2017-082613 gran

On the convex characterisation of the set of unital quantum channels

In this paper, we consider the convex structure of the set of unital quantum channels. To do this, we introduce a novel framework to construct and characterise different families of low-rank unital quantum maps. In this framework, unital quantum maps are represented as a set of complex parameters on which we impose a set of constraints. The different families of unital maps are obtained by mapping those parameters into the operator representation of a quantum map. For these families, we also introduce a scalar measuring their distance to the set of mixed-unitary maps. We consider the particular case of qutrit channels which is the smallest set of maps for which the existence of non-unitary extremal maps is known. In this setting, we show how our framework generalises the description of well-known maps such as the antisymmetric Werner-Holevo map but also novel families of qutrit maps