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Abstract Adiabatic measurements, followed by feedback and erasure protocols, have often been considered as a model to embody Maxwell’s Demon paradox and to study the interplay between thermodynamics and information processing. Such studies have led to the conclusion, now widely accepted in the community, that Maxwell’s Demon and the second law of thermodynamics can peacefully coexist because any gain provided by the demon must be offset by the cost of performing the measurement and resetting the demon’s memory to its initial state. Statements of this kind are collectively referred to as second laws of information thermodynamics and have recently been extended to include quantum theoretical scenarios. However, previous studies in this direction have made several assumptions, particularly about the feedback process and the demon’s memory readout, and thus arrived at statements that are not universally applicable and whose range of validity is not clear. In this work, we fill this gap by precisely characterizing the full range of quantum feedback control and erasure protocols that are overall consistent with the second law of thermodynamics. This leads us to conclude that the second law of information thermodynamics is indeed universal: it must hold for any quantum feedback control and erasure protocol, regardless of the measurement process involved, as long as the protocol is overall compatible with thermodynamics. Our comprehensive analysis not only encompasses new scenarios but also retrieves previous ones, doing so with fewer assumptions. This simplification contributes to a clearer understanding of the theory.

Observational entropy—a quantity that unifies Boltzmann's entropy, Gibbs' entropy, von Neumann's macroscopic entropy, and the diagonal entropy—was recently argued to play a key role in a modern formulation of statistical mechanics. Here, relying on algebraic techniques taken from Petz's theory of statistical sufficiency and on a Lévy-type concentration bound, we prove rigorous theorems showing how the observational entropy of a system undergoing a unitary evolution chosen at random tends to increase with overwhelming probability and to reach its maximum very quickly. More precisely, we show that for any observation that is sufficiently coarse with respect to the size of the system, regardless of the initial state of the system (be it pure or mixed), random evolution renders its state practically indistinguishable from the uniform (i.e., maximally mixed) distribution with a probability approaching 1 as the size of the system grows. The same conclusion holds not only for random evolutions sampled according to the unitarily invariant Haar distribution but also for approximate 2-designs, which are thought to provide a more physically and computationally reasonable model of random evolutions.

Observational entropy captures both the intrinsic uncertainty of a thermodynamic state and the lack of knowledge due to coarse-graining. We demonstrate two interpretations of observational entropy, one as the statistical deficiency resulting from a measurement, the other as the difficulty of inferring the input state from the measurement statistics by quantum Bayesian retrodiction. These interpretations show that the observational entropy implicitly includes a uniform reference prior. Since the uniform prior cannot be used when the system is infinite-dimensional or otherwise energy-constrained, we propose generalizations by replacing the uniform prior with arbitrary quantum states that may not even commute with the state of the system. We propose three candidates for this generalization, discuss their properties, and show that one of them gives a unified expression that relates both interpretations.

We construct a resource theory of $sharpness$ for finite-dimensional positive operator-valued measures (POVMs), where the $sharpness-non-increasing$ operations are given by quantum preprocessing channels and convex mixtures with POVMs whose elements are all proportional to the identity operator. As required for a sound resource theory of sharpness, we show that our theory has maximal (i.e., sharp) elements, which are all equivalent, and coincide with the set of POVMs that admit a repeatable measurement. Among the maximal elements, conventional non-degenerate observables are characterized as the canonical ones. More generally, we quantify sharpness in terms of a class of monotones, expressed as the EPR–Ozawa correlations between the given POVM and an arbitrary reference POVM. We show that one POVM can be transformed into another by means of a sharpness-non-increasing operation if and only if the former is sharper than the latter with respect to all monotones. Thus, our resource theory of sharpness is $complete$, in the sense that the comparison of all monotones provides a necessary and sufficient condition for the existence of a sharpness-non-increasing operation between two POVMs, and $operational$, in the sense that all monotones are in principle experimentally accessible.

This article analyses the multimodal construction of various global TV formats and the modes through which the format negotiates reinforcement of its ideological bases, innovation, change and unlimited semiosis. Theoretically, this work draws on social semiotics, multimodality and political economy. Methodologically, it applies semiotic analysis to really popular global formats. The results show that the format is an extraordinary and powerful example of multimodality which speaks the global language of signs. On the one hand, different languages and forms of communication reinforce its ideologies, such as competition, primacy of money, objectification of human bodies and consumerism; but the format also puts forward a kind of self-propaganda; in many cases, in fact, its communication aims to support and promote itself, even when this contradicts other messages of the system; it is by being successful that producers make more money, become more successful, may further influence the audience, and so on. On the other hand, the languages and the forms adopted continually renew the format, change the relationships between signifier and signified, and create new symbols. This unlimited semiosis allows the format to refresh or adapt its image, get more audience and remain competitive in the market.

The Cultural Non-human Animal. Analysing Italo Calvino’s Italian Fairy Tales with Zoosemiotics. This article analyses traditional Italian fairy tales retold by Italo Calvino in 1956 and their relationships to nature and culture. Zoosemiotics, a branch of both semiotics and animal studies, argues that nature and culture are not separated and in contrast and that, instead, culture is a limited part of nature. This conceptual change envisions different relationships between humans and animals as well as more broadly the end of animal anthropomorphism. Methodologically, the article applies a zoosemiotic analysis to the Italian fairy tales retold by Calvino. The article concludes that some animals in the fairy tales are still anchored to the old view while others move towards the cultural terrain, showing cultural attitudes and inhabiting a cultural area usually reserved for human animals. This shift leads to an inverted semiotic destiny of humans and animals in fairy tales: while animals are traditionally represented as symbols, Calvino’s rewriting turns them into icons, representing only themselves, marked by a neat individuality and independence from their species; while humans are, conversely, usually represented as icons, Calvino’s stories turn them into symbols, such as ingratitude or jealousy. The article shows the usefulness of zoosemiotics and nature/culture in analysing non human-animals in fairy tales and adds to earlier studies considering non-human animals in Calvino’s fairy tales as an epitome of Anthropocene. Article history: Received 2 February 2022; Revised 5 May 2022; Accepted 24 May 2022; Available online 30 June 2022; Available print 30 June 2022. REZUMAT. Animalul cultural non-uman. O analiză a poveștilor lui Italo Calvino cu ajutorul zoosemioticii. Articolul de față analizează povești italiene tradiționale repovestite de către Italo Calvino în 1956, precum și relația lor cu natura și cultura. Zoosemiotica, o ramură atât a semioticii cât și a studiilor despre animale, argumentează că natura și cultura nu sunt separate și nu se află în contrast, ci că, dimpotrivă, cultura este o parte limitată a naturii. Această schimbare conceptuală preconizează relații diferite între oameni și animale, precum și, în sens mai general, sfârșitul antropomorfismului animalelor. Metodologic, articolul aplică o analiză zoosemiotică poveștilor italiene repovestite de Calvino. Articolul conchide că anumite povești cu animale sunt încă ancorate într-o viziune mai veche, în timp ce altele se deplasează către un teren cultural, demonstrând atitudini culturale și populând aria culturală rezervată de obicei animalelor umane. Această schimbare conduce la un destin semiotic inversat al oamenilor și animalelor în povești: în vreme ce animalele sunt în mod tradițional reprezentate ca simboluri, rescrierea lui Calvino le transformă în icon-uri, ele reprezentându-se doar pe sine, marcate de o individualitate și de o independență distincte față de specia lor, în timp ce oamenii, de obicei reprezentați ca icon-uri, sunt transformați în povestirile lui Calvino în simboluri, de pildă ale ingratitudinii ori geloziei. Articolul arată utilitatea zoosemioticii și binomului natură/cultură în analiza animalelor non-umane în povești, și aduce contribuții la studiile anterioare despre animalele non-umane în poveștile lui Calvino ca întruchipare a Antropocenului. Cuvinte-cheie: studii despre animale, povești, Italo Calvino, zoosemiotică, natură și cultură, antropomorfism, Motanul încălțat

While there is general consensus on the definition of incompatible POVMs, moving up to the level of instruments one finds a much less clear situation, with mathematically different and logically independent definitions of incompatibility. Here we close this gap by introducing the notion of $q-compatibility$, which unifies different notions of POVMs, channels, and instruments incompatibility into one hierarchy of resource theories of communication between separated parties. The resource theories that we obtain are $complete$, in the sense that they contain complete families of free operations and monotones providing necessary and sufficient conditions for the existence of a transformation. Furthermore, our framework is fully $operational$, in the sense that free transformations are characterized explicitly, in terms of local operations aided by causally-constrained directed classical communication, and all monotones possess a game-theoretic interpretation making them experimentally measurable in principle. We are thus able to pinpoint exactly what each notion of incompatibility consists of, in terms of information-theoretic resources.

We propose a category-theoretic definition of retrodiction and use it to exhibit a time-reversal symmetry for all quantum channels. We do this by introducing retrodiction families and functors, which capture many intuitive properties that retrodiction should satisfy and are general enough to encompass both classical and quantum theories alike. Classical Bayesian inversion and all rotated and averaged Petz recovery maps define retrodiction families in our sense. However, averaged rotated Petz recovery maps, including the universal recovery map of Junge-Renner-Sutter-Wilde-Winter, do not define retrodiction functors, since they fail to satisfy some compositionality properties. Among all the examples we found of retrodiction families, the original Petz recovery map is the only one that defines a retrodiction functor. In addition, retrodiction functors exhibit an inferential time-reversal symmetry consistent with the standard formulation of quantum theory. The existence of such a retrodiction functor seems to be in stark contrast to the many no-go results on time-reversal symmetry for quantum channels. One of the main reasons is because such works defined time-reversal symmetry on the category of quantum channels alone, whereas we define it on the category of quantum channels and quantum states. This fact further illustrates the importance of a prior in time-reversal symmetry.

Observational entropy provides a general notion of quantum entropy that appropriately interpolates between Boltzmann’s and Gibbs’ entropies, and has recently been argued to provide a useful measure of out-of-equilibrium thermodynamic entropy. Here we study the mathematical properties of observational entropy from an information-theoretic viewpoint, making use of recently strengthened forms of the monotonicity property of quantum relative entropy. We present new bounds on observational entropy applying in general, as well as bounds and identities related to sequential and post-processed measurements. A central role in this work is played by what we call the ‘coarse-grained’ state, which emerges from the measurement’s statistics by Bayesian retrodiction, without presuming any knowledge about the ‘true’ underlying state being measured. The degree of distinguishability between such a coarse-grained state and the true (but generally unobservable) one is shown to provide upper and lower bounds on the difference between observational and von Neumann entropies.

Von Neumann obtained the formula for the entropy of a quantum state by assuming the validity of the second law of thermodynamics in a thought experiment involving semipermeable membranes and an ideal gas of quantum-labeled particles. Despite being operational for the most part, von Neumann's argument departs from an operational narrative in its use of the spectral theorem. In this work, we show that the role of the spectral theorem in von Neumann's argument can be taken over by the operational assumptions of repeatability and reversibility, and, using these, we are able to explore the consequences of the second law also in theories that do not possess a unique spectral decomposition. As a byproduct, we obtain the Groenewold-Ozawa information gain as a natural monotone for a suitable ordering of instruments, providing it with an operational interpretation valid in quantum theory and beyond.

Quantum error correction (QEC) is a procedure by which the quantum state of a system is protected against a known type of noise, by preemptively adding redundancy to that state. Such a procedure is commonly used in quantum computing when thermal noise is present. Interestingly, thermal noise has also been known to play a central role in quantum thermodynamics (QTD). This fact hints at the applicability of certain QTD statements in the QEC of thermal noise, which has been discussed previously in the context of Maxwell’s demon. In this paper, we view QEC as a quantum heat engine with a feedback controller (i.e., a demon). We derive an upper bound on the measurement heat dissipated during the error-identification stage in terms of the Groenewold information gain, thereby also providing the latter with a physical meaning when it is negative. Further, we derive the second law of thermodynamics in the context of this QEC engine, operating with general quantum measurements. Finally, we show that, under a set of physically motivated assumptions, this leads to a fundamental triple-trade-off relation, which implies a trade-off between the maximum achievable fidelity of QEC and the super-Carnot efficiency that heat engines with feedback controllers have been known to possess. A similar trade-off relation occurs for the thermodynamic efficiency of the QEC engine and the efficacy of the quantum measurement used for error identification.

Similarly to entropy, majorization allows to quantify deviation from uniformity in a wide range of fields. In this paper, the authors use its generalization to the quantum realm to derive a complete set of necessary and sufficient conditions for thermal transformations of quantum states.

In space-like separated experiments and other scenarios where multiple parties share a classical common cause but no cause-effect relations, quantum theory allows a variety of nonsignaling resources which are useful for distributed quantum information processing. These include quantum states, nonlocal boxes, steering assemblages, teleportages, channel steering assemblages, and so on. Such resources are often studied using nonlocal games, semiquantum games, entanglement-witnesses, teleportation experiments, and similar tasks. We introduce a unifying framework which subsumes the full range of nonsignaling resources, as well as the games and experiments which probe them, into a common resource theory: that of local operations and shared randomness (LOSR). Crucially, we allow these LOSR operations to locally change the type of a resource, so that players can convert resources of $any$ type into resources of any other type, and in particular into strategies for the specific type of game they are playing. We then prove several theorems relating resources and games of different types. These theorems generalize a number of seminal results from the literature, and can be applied to lessen the assumptions needed to characterize the nonclassicality of resources. As just one example, we prove that semiquantum games are able to perfectly characterize the LOSR nonclassicality of every resource of $any$ type (not just quantum states, as was previously shown). As a consequence, we show that any resource can be characterized in a measurement-device-independent manner.

The Alberti-Uhlmann criterion states that any given qubit dichotomy can be transformed into any other given qubit dichotomy by a quantum channel if and only if the testing region of the former dichotomy includes the testing region of the latter dichotomy. Here, we generalize the Alberti-Uhlmann criterion to the case of arbitrary number of qubit or qutrit states. We also derive an analogous result for the case of qubit or qutrit measurements with arbitrary number of elements. We demonstrate the possibility of applying our criterion in a semi-device independent way.

We characterize the operational capabilities of quantum channels which can neither create nor detect quantum coherence vis-à-vis efficiently manipulating coherence as a resource. We study the class of dephasing-covariant operations (DIO), unable to detect the coherence of any input state, as well as introduce an operationally motivated class of channels ρ-DIO, which is tailored to a specific input state. We first show that pure-state transformations under DIO are completely governed by majorization, establishing necessary and sufficient conditions for such transformations and adding to the list of operational paradigms where majorization plays a central role. We then show that ρ-DIO are strictly more powerful: although they cannot detect the coherence of the input state ρ, the operations ρ-DIO can distill more coherence than DIO. However, the advantage disappears in the task of coherence dilution as well as generally in the asymptotic limit, where both sets of operations achieve the same rates in all transformations.

Given two pairs of quantum states, we want to decide if there exists a quantum channel that transforms one pair into the other. The theory of quantum statistical comparison and quantum relative majorization provides necessary and sufficient conditions for such a transformation to exist, but such conditions are typically difficult to check in practice. Here, by building upon work by Keiji Matsumoto, we relax the problem by allowing for small errors in one of the transformations. In this way, a simple sufficient condition can be formulated in terms of one-shot relative entropies of the two pairs. In the asymptotic setting where we consider sequences of state pairs, under some mild convergence conditions, this implies that the quantum relative entropy is the only relevant quantity deciding when a pairwise state transformation is possible. More precisely, if the relative entropy of the initial state pair is strictly larger compared to the relative entropy of the target state pair, then a transformation with exponentially vanishing error is possible. On the other hand, if the relative entropy of the target state is strictly larger, then any such transformation will have an error converging exponentially to one. As an immediate consequence, we show that the rate at which pairs of states can be transformed into each other is given by the ratio of their relative entropies. We discuss applications to the resource theories of athermality and coherence, where our results imply an exponential strong converse for general state interconversion.

Given a physical device as a black box, one can in principle fully reconstruct its input–output transfer function by repeatedly feeding different input probes through the device and performing different measurements on the corresponding outputs. However, for such a complete tomographic reconstruction to work, full knowledge of both input probes and output measurements is required. Such an assumption is not only experimentally demanding, but also logically questionable, as it produces a circular argument in which the characterization of unknown devices appears to require other devices to have been already characterized beforehand. Here, we introduce a method to overcome such limitations present in usual tomographic techniques. We show that, even without any knowledge about the tomographic apparatus, it is still possible to infer the unknown device to a high degree of precision, solely relying on the observed data. This is achieved by employing a criterion that singles out the minimal explanation compatible with the observed data. Our method, that can be seen as a data-driven analog of tomography, is solved analytically and implemented as an algorithm for the learning of qubit channels.

We provide a complete set of game-theoretic conditions equivalent to the existence of a transformation from one quantum channel into another one, by means of classically correlated preprocessing and postprocessing maps only. Such conditions naturally induce tests to certify that a quantum memory is capable of storing quantum information, as opposed to memories that can be simulated by measurement and state preparation (corresponding to entanglement-breaking channels). These results are formulated as a resource theory of genuine quantum memories (correlated in time), mirroring the resource theory of entanglement in quantum states (correlated spatially). As the set of conditions is complete, the corresponding tests are faithful, in the sense that any non-entanglement-breaking channel can be certified. Moreover, they only require the assumption of trusted inputs, known to be unavoidable for quantum channel verification. As such, the tests we propose are intrinsically different from the usual process tomography, for which the probes of both the input and the output of the channel must be trusted. An explicit construction is provided and shown to be experimentally realizable, even in the presence of arbitrarily strong losses in the memory or detectors.

GIS4EU In Europe, spatial information is characterised by lack of harmonisation between datasets at different geographical scales, fragmented datasets and sources, gaps in availability and duplication of information. In this context the GIS4EU project aim is to create a common knowledge base and make spatial information more accessible according to standards and requirements of the INSPIRE Directive. Therefore, the project intends to develop a common data model in order to enable access to consistent and homogenous reference data provided by cartographic authorities of different countries and levels.