On a block matrix inequality quantifying the monogamy of the negativity of entanglement

We convert a conjectured inequality from quantum information theory, due to He and Vidal, into a block matrix inequality and prove a very special case. Given n matrices Ai, i = 1,..., n, of the same size, let Z1 and Z2 be the block matrices Z1 := ( A j A* i) n i, j= 1 and Z2 := ( A* j Ai) n i, j= 1, respectively. Then, the conjectured inequality is (|| Z1|| 1 - Tr Z1) 2 + (|| Z2|| 1 - Tr Z2) 2 =.. ( i ) = j || Ai || 2|| A j || 2.. 2, where || . || 1 and || . || 2 denote the trace norm and the Hilbert- Schmidt norm, respectively. We prove this inequality for the already challenging case n = 2 with A1 = I

Entanglement-enhanced testing of multiple quantum hypotheses

Quantum hypothesis testing has been greatly advanced for the binary discrimination of two states, or two channels. In this setting, we already know that quantum entanglement can be used to enhance the discrimination of two bosonic channels. Here, we remove the restriction of binary hypotheses and show that entangled photons can remarkably boost the discrimination of multiple bosonic channels. More precisely, we formulate a general problem of channel-position finding where the goal is to determine the position of a target channel among many background channels. We prove that, using entangled photons at the input and a generalized form of conditional nulling receiver at the output, we may outperform any classical strategy. Our results can be applied to enhance a range of technological tasks, including the optical readout of sparse classical data, the spectroscopic analysis of a frequency spectrum, and the determination of the direction of a target at fixed range

Fundamental limits to quantum channel discrimination

What is the ultimate performance for discriminating two arbitrary quantum channels acting on a finite-dimensional Hilbert space? Here we address this basic question by deriving a general and fundamental lower bound. More precisely, we investigate the symmetric discrimination of two arbitrary qudit channels by means of the most general protocols based on adaptive (feedback-assisted) quantum operations. In this general scenario, we first show how port-based teleportation can be used to simplify these adaptive protocols into a much simpler non-adaptive form, designing a new type of teleportation stretching. Then, we prove that the minimum error probability affecting the channel discrimination cannot beat a bound determined by the Choi matrices of the channels, establishing a general, yet computable formula for quantum hypothesis testing. As a consequence of this bound, we derive ultimate limits and no-go theorems for adaptive quantum illumination and single-photon quantum optical resolution. Finally, we show how the methodology can also be applied to other tasks, such as quantum metrology, quantum communication and secret key generation

Relative entanglement entropies in 1 + 1-dimensional conformal field theories

We study the relative entanglement entropies of one interval between excited states of a 1+1 dimensional conformal field theory (CFT). To compute the relative entropy S(\u3c11\u2016\u3c10) between two given reduced density matrices \u3c11 and \u3c10 of a quantum field theory, we employ the replica trick which relies on the path integral representation of Tr(\u3c11\u3c1n 1210) and define a set of R\'enyi relative entropies Sn(\u3c11\u2016\u3c10). We compute these quantities for integer values of the parameter n and derive via the replica limit, the relative entropy between excited states generated by primary fields of a free massless bosonic field. In particular, we provide the relative entanglement entropy of the state described by the primary operator i 02\u3d5, both with respect to the ground state and to the state generated by chiral vertex operators. These predictions are tested against exact numerical calculations in the XX spin-chain finding perfect agreement. \ua9 2017, The Author(s)

NoMa-hanke: luonnonkuitujen 3D-tulostamisen mahdollisuuksia

3D-tulostusala on nopeasti kehittyvä ala. Sen ennustetaan kasvavan nopeasti, yksinkertaisten kotitulostimien halpenemisen ja teollisuuden sovellusten lisääntymisen myötä. Tiedon digitalisoitumisen ja palvelujen kehittymisen myötä 3D-tulostaminen sekä 3D-tulostettujen tavaroiden hankinta sekä kustomointi omien tarpeiden mukaan helpottuu alasta ja tekniikoista perehtymättömillekin. Opinnäytetyön tavoitteena oli selvittää TEKES:n vuosina 2015-2017 rahoittamassa, NoMa-hankkeessa tutkittavien luonnonkuitujen 3D-tulostamisen mahdollisuuksia 3D-tulostustekniikoiden, materiaalikehityksen, digitaalisen toimintaympäristön sekä niiden ympärille kehittyvän liiketoiminnan brändäämisen näkökulmista. Luonnonkuitupohjaiset biokomposiitit ovat yksi kehittyvä osa-alue 3D-tulostusmateriaaleissa. Luonnonkuiduilla on mahdollista saavuttaa jäykkyyttä materiaaliin sekä luonnonmateriaalin, kuten puun kaltainen ulkonäkö ja tuntu valmistettavaan kappaleeseen, riippuen komposiittiin lisättävästä kuidusta ja määrästä. Yleisimmin 3D-tulostusmateriaaleissa käytetyt sideaineet ovat joko öljypohjaisia tai kasvipohjaisia polymeerejä. Luonnonkuitujen avulla on mahdollista parantaa kasvipohjaisten sideaineiden maatumista sekä vähentää öljypohjaisten sideaineiden kulutusta käyttämällä luonnonkuituja täyteaineena. Kiertotalouden kannalta luonnonkuitupohjaiset biokomposiittit ovat tällä hetkellä ongelmallisia, sillä luonnonkuidut vaikeuttavat uudelleen prosessointia. Uuden luonnonkuitupohjaisen 3D-tulostusmateriaalin ja sen ympärille rakentuvan liiketoiminnan brändäämistä varten vertailtiin ja analysoitiin markkinoilla jo olevia biokomposiittimateriaalin valmistajia. Yritysten verkkosivustoihin ja sosiaalisen median kanaviin perustuvassa vertailussa havaittiin, että monilla yrityksillä, jotka valmistavat biokomposiittimateriaaleja, ympäristöystävällisyys ja erikoistuminen biomateriaaleihin olivat heikosti esillä brändin visioissa ja arvoissa. Monien vertailtujen yritysten visuaalinen ilme oli suunnattu lähinnä alan ammattilaisille. Luonnonkuitupohjaisten komposiittimateriaalien ympärille kehitettävän liiketoiminnan brändin tulisi viestiä selkeästi ja johdonmukaisesti ympäristömyönteisyydestä sekä olla helposti lähestyttävä jokaiselle.3D printing industry is developing fast and is forecasted to grow rapidly due lowering price of simple 3D printers for the home market and the increase of industrial adaptation. The digitalization of information and the development of services are leading to a situation, where 3D printing and acquisition and customization of 3D printed things is getting easier for non-professionals also. The subject of this thesis was to clarify the potential of 3D printed natural fibers that are studied in TEKES (2015-2017) funded NoMa-project, from the perspective of development of 3D printing, materials, digital operating environment and branding of bio based 3D printing materials and services. Natural fibre based bio composites are one of the developing sectors in 3D printing materials. Depending on the amount and quality of natural fibres, material strength increase and natural, for example wood like looks are possible to achieve with natural fibres in bio composites. There are many possibilities for bio composite constructions. Most common base materials for composites are either oil based or bio based polymers. Better composting properties are achieved by adding natural fibres to bio based polymer such as polylactic acid. By adding natural fibres to oil based polymers as fillers, it is possible to decrease the use of non-biodegradable materials. In terms of circular economy, bio composites can be problematic, since natural fibres affect negatively to the re-production process. For branding of new natural fibre based 3D printing material and business based on it, a comparison and analyzation of bio based material brands, that are already in the market, was conducted. Main findings of the comparison were that environmental friendliness and specialization for bio based materials was not very clearly visible in the vision and values of brands. Many of the analysed brands visual image was also pointed mainly for 3D printing professionals. A new brand for natural fibre based material or service should give a clear and consistent message from environment friendliness and it must be easily approachable for everybody