One of the purposes of this work was to provide an introduction to the field of **quantum** **information** theory. We began studying the classical theory of informa- tion **in** Ch. 2. We have introduced the Shannon entropy and seen two different interpretations for it. From one perspective, the Shannon entropy measures the amount of **information** (uncertainty) of a message (random variable) and, from the other, it tells us the minimum amount of binary digits needed to encode faithfully a given message. Then, we discussed two-messages entropies, the mutual informa- tion, which measures the **correlations** between two messages or the **information** they share **in** common; the conditional entropy, which gives the amount of **information** we have about some message when we have a previous knowledge of another; the joint entropy, which measures the non-redundant **information** of two messages; and the relative entropy, which measures the loss of **information** when we use an ap- proximate message instead of the original. Then, **in** Ch. 3 we reviewed some basic concepts **in** **quantum** mechanics as well as introduced some more advanced ones such as the dynamics of open **quantum** systems and generalized measurement dynamics. **In** Ch. 4 we begin our exploration of **quantum** **information**. We began considering the von Neumann entropy and saw that it is the analogous of Shannon entropy **in** the **quantum** realm. **In** other words, it gives the amount of qubits necessary to transmit (transpose) faithfully a **quantum** signal (density operator). Then, we studied the concept of **correlations** **in** **quantum** theory as well as developed some measures of **quantum** **correlations**. For pure bipartite states, we can measure the entanglement with the entropy of entanglement, the purity or the Schmidt rank. For mixed states, we measure the amount of **correlations** with the entanglement of formation, the concurrence, the **quantum** mutual **information** and the **quantum**

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However, recent developments **in** the field of new materials have led to observe and control **quantum** systems at different times, length scales and energy ranges (BREUER et al., 2016; VEGA; ALONSO, 2017). **In** many of these scenarios, a large separation between system and environment time scales can no longer be assumed, leading to non- Markovian behavior and eventually a back-flow of **information** from the environment into the system. Indeed, the Markovian behavior is always an idealization **in** the de- scription of the **quantum** dynamics, with non-Markovianity being non-negligible **in** a number of different scenarios, such as biological (ISHIZAKI; FLEMING, 2009; REBEN- TROST; CHAKRABORTY; ASPURU-GUZIK, 2009; LIANG, 2010; CHEN et al., 2015) or condensed matter systems (WOLF et al., 2008; APOLLARO et al., 2011; HAIKKA; JOHNSON; MANISCALCO, 2013). A considerable amount of literature has been published on rigorously define non-Markovian dynamics **in** the **quantum** case, different approaches have been followed and several methods have been proposed (see, e. g., (RIVAS; HUELGA; PLENIO, 2014; POLLOCK et al., 2015; POLLOCK et al., 2018; BREUER et al., 2016; VEGA; ALONSO, 2017)). From an applied point of view, non-Markovian dynamics may be a resource for **quantum** tasks through an increase **in** the capacities of **quantum** channels (BYLICKA; CHRUŚCIŃSKI; MANISCALCO, 2014). Moreover, it also exhibits applications **in** fault-tolerant **quantum** computation (AHARONOV; KITAEV; PRESKILL, 2006). Basically, two main questions need to be discussed **in** this context (RIVAS; HUELGA; PLENIO, 2014):

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Most works on open **quantum** systems generally focus on the reduced physical system by tracing out the environment degrees of freedom. Here we show that the qubit distributions with the environment are essential for a thorough analysis, and demonstrate that the way that **quantum** **correlations** are distributed **in** a **quantum** register is constrained by the way **in** which each subsystem gets correlated with the environment. For a two-qubit system coupled to a common dissipative environment E, we show how to optimise interqubit **correlations** and entanglement via a quantification of the qubit-environment **information** flow, **in** a process that, perhaps surprisingly, does not rely on the knowledge of the state of the environment. To illustrate our findings, we consider an optically-driven bipartite interacting qubit AB system under the action of E . By tailoring the light-matter interaction, a relationship between the qubits early stage

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It is a relatively new insight of classical statistics that empirical data can contain **information** about causation rather than mere correlation. First algorithms have been proposed that are capable of testing whether a presumed causal relationship is compatible with an observed distribution. However, no systematic method is known for treating such problems **in** a way that generalizes to **quantum** systems. Here, we describe a general algorithm for computing **information**–theoretic constraints on the **correlations** that can arise from a given causal structure, where we allow for **quantum** systems as well as classical random variables. The general technique is applied to two relevant cases: ﬁrst, we show that the principle of **information** causality appears naturally **in** our framework and go on to generalize and strengthen it. Second, we derive bounds on the **correlations** that can occur **in** a networked architecture, where a set of few-body **quantum** systems is distributed among some parties.

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The authors are grateful to Elie Wolfe, Peter Wittek, Flavio Baccari, and Marco Túlio Quintino for insightful discussions. This work is supported by the ERC CoG QITBOX, the AXA Chair **in** **Quantum** **Information** Science, Fundacio Obra Social “la Caixa” (LCF/BQ/ ES15/10360001), the Spanish MINECO (QIBEQI FIS2016-80773-P and Severo Ochoa SEV-2015-0522), Fundacio Cellex, Generalitat de Catalunya (CERCA Program and SGR1381), the John Templeton Foundation via the Grant Q-CAUSAL No. 61084, the Serrapilheira Institute (Grant No. Serra-1708-15763), the São Paulo Research Foundation FAPESP (Grant No. 2018/07258-7), the Brazilian National Council for Scientific and Technological Development (CNPq) via the National Institute for Science and Technology on **Quantum** **Information** (INCT-IQ) and Grants No. 307172/ 2017-1 and No. 406574/2018-9, the Brazilian agencies MCTIC and MEC, the Austrian Science Fund (FWF) standalone Project No. P 30947, and the Foundation for Polish Science (IRAP project, ICTQT, Contract No. 2018/ MAB/5, cofinanced by EU within Smart Growth Operational Programme).

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Parallel to these developments, theoretical studies an- alyzing the role played by relativity **in** the behavior of **quantum** systems when (i) the relative motion and (ii) proper acceleration of the communicating partners is large have attracted much attention (see Ref. [17] for a recent review). This is not only interesting **in** its own right but may also have practical importance because of new trends of implementing **quantum**-**information** protocols at global scales through the use of satellite systems [18–22]. Concerning condition (i), the remarkable fact was shown **in** Ref. [23] that the von Neumann entropy associated with the reduced spin-density matrix of a single particle is not Lorentz invariant. This is so because, **in** general, the spin is Wigner rotated under Lorentz boosts **in** a direction which depends on the particle momentum, thus entangling both degrees of freedom. Similarly, it was shown that the entanglement for a two-particle spin system is not Lorentz invariant either [24]. The Lorentz invariance of the entanglement distillability of a bipartite mixed spin state was investigated **in** Ref. [25]. The degree of violation of the Clauser-Horne-Shimony-Holt inequality as seen by

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The control of **quantum** **correlations** **in** solid state systems by means of material engineering is a broad avenue to be explored, since it makes possible steps toward to the limits of **quantum** mechanics and design of novel materials with applications on emerging **quantum** technologies. **In** this context, this Letter explores the potential of molecular magnets to be prototypes of materials for **quantum** **information** technology. More precisely, we engineered a material and from its geometric **quantum** discord we found significant **quantum** **correlations** up to 9.540 K (even without entanglement); and, **in** addition, a pure singlet state occupied up to 83 K (above liquid nitrogen temperature). These results could only be achieved due to the carboxylate group promoting a metal-to-metal huge magnetic interaction.

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constituents. Therefore, **in** addition to the traditional ways of witnessing **quantum** phase transitions, it has been recently suggested that the tools of **quantum** **information** theory [ 3 ] can also be exploited to characterize the transition points (TPs) of **quantum** phase transitions. Especially, **in** **quantum** spin models, the behavior of entanglement [ 4 ], **quantum** discord [ 5 ], and many other correlation measures have been investigated, and their performance **in** detecting the TPs of the QPTs have been discussed [ 6 , 7 ]. Recently, a new line of research has emerged that concerns itself with the characterization and quantification of **quantum** coherence contained **in** a **quantum** state [ 8 – 12 ]. Based on these new **quantum** coherence measures, similar analysis have been done **in** the ground states of several spin chains [ 7 ]. However, many of these studies focusing on **quantum** **correlations** **in** spin chains have been done for spin-1/2 systems [ 6 , 7 ], where analytical solutions are available **in** many cases. On the other hand, spin-1 models have richer phase diagrams and show more complex physical phenomena, yet methods for obtaining the ground state of such systems are rather more involved [ 13 – 30 ]. For instance, a very important distinctive property of the integer-spin **quantum** systems as compared to the half-integer ones is the Haldane conjecture, which states that the system has a gapped ground state, giving rise to the so-called Haldane phase [ 31 ].

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The parameter ', Eq. (3) represents the phase difference of electrons passing through the upper and the lower arms of the ring. **In** Eq. (1), V (r) is the effective potential for trans- mission of electrons through the **quantum** dot which depends, mainly, on the tunnel barrier between the **quantum** dot and the lead. Applying external magnetic field, B, normal to the plane of the device, then the Aharonov-Bohm phase picked up by an electron encircling this magnetic flux is given by

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We report an experimental implementation of automated state transformations on spatial photonic qutrits following the theoretical proposal made by Baldijão et al. [ Phys. Rev. A 96 , 032329 ( 2017 )]. A qutrit state is simulated by using three Gaussian beams, and after some state operations, the transformed state is available **in** the end **in** terms of the basis state. The state transformation setup uses a spatial light modulator and a calcite-based interferometer. The results reveal the usefulness of the operation method. The experimental data show a good agreement with theoretical predictions, opening possibilities for explorations **in** higher dimensions and **in** a wide range of applications. This is a necessary step **in** qualifying spatial photonic qudits as a competitive setup for experimental research **in** the implementation of **quantum** algorithms which demand a large number of steps. DOI: 10.1103/PhysRevA.97.022301

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Neste artigo, discutem-se os conceitos de copyleft e de licenças criativas de uso de informação e outros bens imateriais, como forma inovadora de relação contratual entre produtores [r]

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Numerical consequences. Numerical values of the state vector Y(x,n) have been obtained for a large number of initial conditions g, different choices of coin operator angle h, and system size 2L 1 1. For the sake of definitiveness, we always consider x g [2L,L]. The asymptotic magnetization depends on the values of both g and h, as illustrated by the curves M|g and M|h **in** Fig. 1. It is possible to see that the numerical values corroborate the analytical expressions given above. For arbitrary initial combinations of up and down components, the typical patterns change continuously from one of the extreme cases to the other. The extreme values of M, which depend on the initial conditions, lie **in** the interval 1{ p ﬃﬃﬃ 2 2,1
. **In** Fig. 1b we illustrate the dependence of M|g. It is amazing to see that, by an adequate choice of the coin operator (through the selected value of h), it is

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Although no pratical implementation or experiment was made, **in** the same paper, the authors introduce the concept of Block Reuse 2 . They argue that it is possible to optimize the protocol by maintaining a record of all subblocks exchanged during BINARY executions and also using them for the cascade effect. That is, after the first iteration, upon correcting one error, instead of adding to the set of blocks to correct just the block from each iteration containing the corrected index, every subblock containing that index that was exchanged during the BINARY protocol should also be added to the set. As these blocks will be smaller, fewer parity exchanges will be needed to correct an error.

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This theorem already hints of a theme that shall be recurrent **in** the search for ontological models: we can **in** fact make ontological models for **quantum** theory, and **in** fact we can make them almost **in** any way that we like, but there’s a price to pay: the various aspects of the model become more and more intertwined. We can’t really talk of independent **quantum** systems, separation between state and experiment, nor even (as we shall see **in** the next section) talk about a measurement outcome without talking about the whole experiment. Of course, this bodes very badly for the idea of ontological models: **in** the extreme limit of this interdependence our ontological model only lists possible experiments and their results, without ever trying to make sense of them **in** a simpler and more general theory. A model like this wouldn’t be falsifiable by its very nature, but precisely because of this it is a perversion of the scientific method [19], and should therefore be rejected on methodological grounds.

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Skozi predstavitev vizualizacije informacij smo pravzaprav odgovarjali na neka- tera osnovna vprašanja, ki se zastavljajo ob srečanju s tematiko: zakaj, kako **in** kaj. Pregled študij je pokazal, da odgovor na nobeno izmed zastavljenih vprašanj ni enoznačen ali prav gotovo ne preprost. Rezultati študij **in** eksperimentov niso naklonjeni vizualizaciji **in** le malo poskusov je v resnici zaživelo, pa vendar se zdi, da raziskovalci še vedno verjamejo v moč vizualizacije. Song (2000) to do- bro opiše z besedami, da kljub vsemu ve, da vizualizacija lahko pomaga uporab- nikom, le da za zdaj še nismo odkrili pravega načina. Morda pa se čas vizualiza- cije šele začenja, saj se spletna orodja (**in** s tem tudi ljudje?) vse bolj premikajo k vizualnim podobam. Tudi sami sistemi za poizvedovanje so v zadnjem letu naredili velik preskok v obvladovanju **in** predstavljanju rezultatov **in** ne more- mo zanikati potencialne uporabnosti vizualizacije ter dejstva, da so morda sedaj, bolj kot kdajkoli prej, pripravljeni za nadgradnjo v obliki vizualizacije odnosov **in** povezav med dokumenti.

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excitation, such that m~0. The estimated mean degree is consistent with many different topologies. Let us consider the case of a uniform random network of 15000 neurons with connection probability 0.1. For comparison we also look at a densely connected subnetwork of just 2500 neurons with a connection probability of 0.6. The first model results **in** a spectral radius r&1:4 for the connectivity matrix G, hence falling **in** the linearly unstable regime. **In** contrast, the second network displays a Figure 9. Patches **in** separate populations selectively affect high-order common input motifs. A: Connection rules for networks with patches. Output connections of a neuron are restricted to a randomly chosen region. B: Average **correlations** depending on patch size. Comparison between random networks, patchy networks with randomly distributed neuron type and separate populations, average across 5 networks, error bars from standard deviation. Only separate populations lead to increased **correlations**. Larger increase occurs for smaller patch-size. Total connection probability p~0:1, other parameters as **in** Figure 2. C: Contributions of different motifs. Differences to random networks occur only **in** common input terms of higher order. Patch size S~600.

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