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The understanding of open quantum systems is crucial for the development of quantum technologies. Of particular relevance is the characterisation of divisible quantum dynamics, seen as a generalisation of Markovian processes to the quantum setting. Here, we propose a way to detect divisibility and quantify how non-divisible a quantum channel is through the concept of channel discrimination. We ask how well we can distinguish generic dynamics from divisible dynamics. We show that this question can be answered efficiently through semidefinite programming, which provides us with an operational and efficient way to quantify divisibility., Comment: 13 pages. 5 figures. Several appendices. Suggestions are welcome!

This work seeks to make explicit the operational connection between the preparation of two-level quantum systems with their corresponding description (as states) in a Hilbert space. This may sound outdated, but we show there is more to this connection than common sense may lead us to believe. To bridge these two separated realms -- the actual laboratory and the space of states -- we rely on a paradigmatic mathematical object: the Hopf fibration. We illustrate how this connection works in practice with a simple optical setup. Remarkably, this optical setup also reflects the necessity of using two charts to cover a sphere. Put another way, our experimental realization reflects the bi-dimensionality of a sphere seen as a smooth manifold., Comment: 10 pages, 2 figures, minor adjustments and a section added according to reviewer's suggestions

Non-Markovianty of open quantum systems dynamics is a physically relevant property which is usually associated with the backflow of (quantum) information. Using this paradigmatic marker, we develop an operational framework to investigate how non-Markovianity for qubit dynamics can be distilled when many copies of the channels are used, possibly allowing for a stronger effect on the backflow of information., Comment: 10 pages, 7 figures

Quantum Darwinism offers an explanation for the emergence of classical objective features -- those we are used to at macroscopic scales -- from quantum properties at the microscopic level. The interaction of a quantum system with its surroundings redundantly proliferates information to many parts of the environment, turning it accessible and objective to different observers. But given that one cannot probe the quantum system directly, only its environment, how to witness whether an unknown quantum property can be deemed objective or not? Here we propose a probabilistic framework to analyze this question and show that objectivity implies a Bell-like inequality. Among several other results, we show quantum violations of this inequality, a device-independent proof of the non-objectivity of quantum correlations that give rise to the phenomenon we name "collective hallucination": observers probing distinct parts of the environment can agree upon their measurement outcome of a given observable but such outcome can be totally uncorrelated from the property of the quantum system that fixed observable should be probing. We also implement an appealing photonic experiment where the temporal degree of freedom of photons is the quantum system of interest, while their polarization acts as the environment. Employing a fully black-box approach, we achieve the violation of a Bell inequality, thus certifying the non-objectivity of the underlying quantum dynamics in a fully device-independent framework.

The no-broadcasting theorem is one of the most fundamental results in quantum information theory; it guarantees that the simplest attacks on any quantum protocol, based on eavesdropping and copying of quantum information, are impossible. Due to its fundamental importance, it is natural to ask whether it is an inherent quantum property or holds also for a broader class of non-classical theories. A relevant generalization is to consider non-signalling boxes. Subsequently Joshi, Grudka and Horodecki$^{\otimes 4}$ conjectured that one cannot locally broadcast nonlocal boxes. In this paper, we prove their conjecture based on fundamental properties of the relative entropy of boxes. Following a similar reasoning, we also obtain an analogous theorem for steerable assemblages., Comment: 9 + 10 pages, 3 figures

Aumann's celebrated theorem says that a group of agents who once shared a common prior probability distribution cannot assign different posteriors to a given proposition, should these agents have common knowledge about their posteriors. In other words, rational agents cannot agree to disagree. Aumann's agreement theorem was one of the first attempts to formalise and explore the role played by common knowledge in decision theory. Recently, we have seen a resurfacing of the debate around possible (quantum) extensions of Aumann's results. This paper contributes to this discussion. First, as expected, we argue that agreeing to disagree is impossible in quantum theory. Secondly, and based on the quantum argument, we show that agreeing to disagree is also forbidden in any generalised probability theory., Comment: Improved version. We welcome suggestions! =)

Machine learning techniques have been successfully applied to classifying an extensive range of phenomena in quantum theory. From detecting quantum phase transitions to identifying Bell non-locality, it has been established that classical machines can learn genuine quantum features via classical data. Quantum entanglement is one of the uniquely quantum phenomena in that range, as it has been shown that neural networks can be used to classify different types of entanglement. Our work builds on this topic. We investigate whether distinct models of neural networks can learn how to detect catalysis and self-catalysis of entanglement. Additionally, we also study whether a trained machine can detect another related phenomenon - which we dub transfer knowledge. As we build our models from scratch, besides making all the codes available, we can study a whole gamut of paradigmatic measures, including accuracy, execution time, training time, bias in the training data set and so on., Comment: We welcome suggestions! =)

The notorious quantum measurement problem brings out the difficulty to reconcile two quantum postulates: the unitary evolution of closed quantum systems and the wave-function collapse after a measurement. This problematics is particularly highlighted in the Wigner's friend thought experiment, where the mismatch between unitary evolution and measurement collapse leads to conflicting quantum descriptions for different observers. A recent no-go theorem has established that the (quantum) statistics arising from an extended Wigner's friend scenario is incompatible when one try to hold together three innocuous assumptions, namely no-superdeterminism, parameter independence and absoluteness of observed events. Building on this extended scenario, we introduce two novel measures of non-absoluteness of events. The first is based on the EPR2 decomposition, and the second involves the relaxation of the absoluteness hypothesis assumed in the aforementioned no-go theorem. To prove that quantum correlations can be maximally non-absolute according to both quantifiers, we show that chained Bell inequalities (and relaxations thereof) are also valid constraints for Wigner's experiment.

Quantum Darwinism proposes that the proliferation of redundant information plays a major role in the emergence of objectivity out of the quantum world. Is this kind of objectivity necessarily classical? We show that if one takes Spekkens' notion of noncontextuality as the notion of classicality and the approach of Brand\~{a}o, Piani and Horodecki to quantum Darwinism, the answer to the above question is `yes', if the environment encodes sufficiently well the proliferated information. Moreover, we propose a threshold on this encoding, above which one can unambiguously say that classical objectivity has emerged under quantum Darwinism., Comment: Essentially the accepted version. Enhanced clarity, but main results stand the same. Addition of two new subsections: 1- a cutoff for classical objectivity 2-state spectrum broadcasting case (+ the relative subsections to the appendix). For the final version, please look at PRX Quantum. 8 pages, 2 figures in the main text + 7 pages, 1 figure in the Appendix. Comments are welcome!

We connect two key concepts in quantum information: compatibility and divisibility of quantum channels. Two channels are compatible if they can be both obtained via marginalization from a third channel. A channel divides another channel if it reproduces its action by sequential composition with a third channel. (In)compatibility is of central importance for studying the difference between classical and quantum dynamics. The relevance of divisibility stands in its close relationship with the onset of Markovianity. We emphasize the simulability character of compatibility and divisibility, and, despite their structural difference, we find a set of channels -- self-degradable channels -- for which the two notions coincide. We also show that, for degradable channels, compatibility implies divisibility, and that, for anti-degradable channels, divisibility implies compatibility. These results motivate further research on these classes of channels and shed new light on the meaning of these two largely studied notions., Comment: Suggestions are welcome! =)

With the birth of quantum information science, many tools have been developed to deal with many-body quantum systems. Although a complete description of such systems is desirable, it will not always be possible to achieve this goal, as the complexity of such description tends to increase with the number of particles. It is thus crucial to build effective quantum theories aiming to understand how the description in one scale emerges from the description of a deeper scale. This contribution explores different mathematical tools to the study of emergent effective dynamics in scenarios where a system is subject to a unitary evolution and the coarse-grained description of it is given by a CPTP map taking the original system into an \emph{effective} Hilbert space of smaller dimension. We see that a well-defined effective dynamics can only be defined when some sort of matching between the underlying unitary and the coarse-graining map is satisfied. Our main goal is to use these different tools to derive necessary and sufficient conditions for this matching in the general case., Comment: Updated Version. Suggestions are welcome! =)

Using Bell-inequalities as a tool to explore non-classical physical behaviours, in this paper we analyze what one can expect to find in many-body quantum physics. Concretely, framing the usual correlation scenarios as a concrete spin-lattice, we want to know whether or not it is possible to violate a Bell-inequality restricted to this scenario. Using clustering theorems, we are able to show that a large family of quantum many-body systems behave almost locally, violating Bell-inequalities (if so) only by a non-significant amount. We also provide examples, explain some of our assumptions via counter-examples and present all the proofs for our theorems. We hope the paper is self-contained., Comment: 12 pages. 3 figures. Comments are welcome!

Quantum networks play a major role in long-distance communication, quantum cryptography, clock synchronization, and distributed quantum computing. Generally, these protocols involve many independent sources sharing entanglement among distant parties that, upon measuring their systems, generate correlations across the network. The question of which correlations a given quantum network can give rise to, remains almost uncharted. Here we show that constraints on the observable covariances, previously derived for the classical case, also hold for quantum networks. The network topology yields tests that can be cast as semidefinite programs, thus allowing for the efficient characterization of the correlations in a wide class of quantum networks, as well as systematic derivations of device-independent and experimentally testable witnesses. We obtain such semidefinite tests for fixed measurement settings, as well as parties that independently choose among collections of measurement settings. The applicability of the method is demonstrated for various networks, and compared with previous approaches., Comment: Similar to the published version

Noncontextuality inequalities are usually derived from the distinguishability properties of quantum states, i.e. their orthogonality. Here, we show that antidistinguishability can also be used to derive noncontextuality inequalities. The Yu-Oh 13 ray noncontextuality inequality can be re-derived and generalized as an instance of our antidistinguishability method. For some sets of states, the antidistinguishability method gives tighter bounds on noncontextual models than just considering orthogonality, and the Hadamard states provide an example of this. We also derive noncontextuality inequalities based on mutually unbiased bases and symmetric informationally complete POVMs. Antidistinguishability based inequalities were initially discovered as overlap bounds for the reality of the quantum state. Our main contribution here is to show that they are also noncontextuality inequalities., Comment: Comments are welcome!

Shedding a new light in the coarse-graining scenario, in this contribution we came up with different necessary and sufficient conditions for the existence of a well-defined coarse-grained state. For doing so, we had to break apart with the usual quantum channels perspective and assume a more decision-theoretical posture. Broadly speaking, we reinterpret the coarse-graining problem in the language of quantum state pooling, and by make an extensive use of the conditional quantum states toolkit we have been able to derive more tangible conditions for the emergence of a compatible, effective coarse-grained state., Comment: Comments are welcome!

Exploring the graph approach, we restate the extended definition of noncontextuality provided by the contextuality-by-default framework. This extended definition avoids the assumption of nondisturbance, which states that whenever two contexts overlap, the marginal distribution obtained for the intersection must be the same. We show how standard tools for characterizing contextuality can also be used in this extended framework for any set of measurements and, in addition, we also provide several conditions that can be tested directly in any contextuality experiment. Our conditions reduce to traditional ones for noncontextuality if the nondisturbance assumption is satisfied., Comment: arXiv admin note: text overlap with arXiv:1710.01318

When the reduced state of a many-body quantum system is independent of its remaining parts, we say it shows what has become known by shielding property. Under some assumptions, equilibrium states of quantum transverse Ising models do manifest such phenomenon. Namely, imagine a many-body quantum system described by a lattice in the presence of an external magnetic field. Suppose there exists a separating interface on this lattice splitting the system into two subsets such that they only interact one another through that interface. In addition, suppose also that the applied external magnetic field is null on the interface. The shielding property states that the reduced state of the set in one side of the interface has no dependence on the Hamiltonian parameters of the set in the other side. This statement was proved in [N. M\'oller et al, PRE 97, 032101 (2018)] for the case where there is only one site in the interface. For lattices with more sites in the interface, it was conjectured that the shielding property is true when the system is in the ground state. For the case of positive temperatures, it does not hold and there are counterexamples to show that. Here we show that the conjecture does hold true for ground states, but under an additional condition. This condition is met, in particular, if the Hamiltonian terms associated to the interface are frustration-free., Comment: 13 pages, 12 figures

Since Bell's theorem we know that quantum mechanics is incompatible with local hidden-variable models, the phenomenon known as quantum nonlocality. However, despite steady progress over the years, precise characterization of the set of quantum correlations remained elusive. There are correlations compatible with the no-signaling principle and still beyond what can be achieved within quantum theory, which has motivated the search for physical principles and computational methods to decide the quantum or postquantum behavior of correlations. Here, we identify a feature of Bell correlations that we call quantum voids: faces of the no-signaling set where all nonlocal correlations are postquantum. Considering the simplest possible Bell scenario, we give a full characterization of quantum voids, also understanding its connections to known principles and its potential use as a dimension witness., Comment: Close to the published version, title modified

Bell's theorem shows that local measurements on entangled states give rise to correlations incompatible with local hidden variable models. The degree of quantum nonlocality is not maximal though, as there are even more nonlocal theories beyond quantum theory still compatible with the nonsignalling principle. In spite of decades of research, we still have a very fragmented picture of the whole geometry of these different sets of correlations. Here we employ both analytical and numerical tools to ameliorate that. First, we identify two different classes of Bell scenarios where the nonsignalling correlations can behave very differently: in one case, the correlations are generically quantum and nonlocal while on the other quite the opposite happens as the correlations are generically classical and local. Second, by randomly sampling over nonsignalling correlations, we compute the distribution of a nonlocality quantifier based on the trace distance to the local set. With that, we conclude that the nonlocal correlations can show concentration phenomena: their distribution is peaked at a distance from the local set that increases both with the number of parts or measurements being performed., Comment: Minor modifications. Still with 13 pages, 8 figures, 5 tables. Comments are welcome!

For any finite number of parts, measurements and outcomes in a Bell scenario we estimate the probability of random $N$-qu$d$it pure states to substantially violate any Bell inequality with uniformly bounded coefficients. We prove that under some conditions on the local dimension the probability to find any significant amount of violation goes to zero exponentially fast as the number of parts goes to infinity. In addition, we also prove that if the number of parts is at least 3, this probability also goes to zero as the the local Hilbert space dimension goes to infinity., Comment: New version. Many modifications and new results. Comments are still welcome!

Contextuality has been identified as a potential resource responsible for the quantum advantage in several tasks. It is then necessary to develop a resource-theoretic framework for contextuality, both in its standard and generalized forms. Here we provide a formal resource-theoretic approach for generalized contextuality based on a physically motivated set of free operations with an explicit parametrisation. Then, using an efficient linear programming characterization for the contextual set of prepared-and-measured statistics, we adapt known resource quantifiers for contextuality and nonlocality to obtain natural monotones for generalized contextuality in arbitrary prepare-and-measure experiments., Comment: 11 pages, 4 figures. Comments are welcome!

We explore the graph approach to contextuality to restate the extended definition of noncontextuality as given by J. Kujala et. al. [Phys. Rev. Lett. 115, 150401 (2015)] using graph-theoretical terms. This extended definition avoids the assumption of the pre-sheaf or non-disturbance condition, which states that if two contexts overlap, then the marginal distribution obtained for the intersection must be the same, a restriction that will never be perfectly satisfied in real experiments. With this we are able to derive necessary conditions for extended noncontextuality for any set of random variables based on the geometrical aspects of the graph approach, which can be tested directly with experimental data in any contextuality experiment and which reduce to traditional necessary conditions for noncontextuality if the non-disturbance condition is satisfied.

The purpose of physics is to describe nature from elementary particles all the way up to cosmological objects like cluster of galaxies and black holes. Although a unified description for all this spectrum of events is desirable, this would be highly impractical. To not get lost in unnecessary details, effective descriptions are mandatory. Here we analyze the dynamics that may emerge from a full quantum description when one does not have access to all the degrees of freedom of a system. More concretely, we describe the properties of the dynamics that arise from quantum mechanics if one has access only to a coarse-grained description of the system. We obtain that the effective maps are not necessarily of Kraus form, due to correlations between accessible and nonaccessible degrees of freedom, and that the distance between two effective states may increase under the action of the effective map. We expect our framework to be useful for addressing questions such as the thermalization of closed quantum systems, as well as the description of measurements in quantum mechanics., Comment: 10 pages, 8 figures. v3: Title changed; minor improvements. Version accepted for publication

In this paper we investigate how common is the phenomenon of Finite Time Disentanglement (FTD) with respect to the set of quantum dynamics of bipartite quantum states with finite dimensional Hilbert spaces. Considering a quantum dynamics from a general sense, as just a continuous family of Completely Positive Trace Preserving maps (parametrized by the time variable) acting on the space of the bipartite systems, we conjecture that FTD happens for all dynamics but those when all maps of the family are induced by local unitary operations. We prove this conjecture valid for two important cases: i) when all maps are induced by unitaries; ii) for pairs of qubits, when all maps are unital. Moreover, we prove some general results about unitaries/CPTP maps preserving product/pure states, Comment: 7 pages and 2 figures. New title. Improved version! Comments are welcome

Conversion of entangled states under (Stochastic) Local Operations and Classical Communication admits the phenomenon of catalysis. Here we explore the possibility of a copy of the initial state itself to perform as a catalyst, which we call a self-catalytic process. We show explicit examples of self-catalysis. Necessary and sufficient conditions for the phenomenon to take place are discussed. We numerically estimate how frequent it is and we show that increasing the number of copies used as catalyst can increases the probability of conversion, but do not make the process deterministic. By the end we conjecture that under LOCC the probability of finding a self-catalytic reaction does not increase monotonically with the dimensions whereas SLOCC does increase., Comment: 13 pages, 7 figures, 4 tables. To appear in J.Phys. A

Non-contextuality (NC) and Bell inequalities can be expressed as bounds $\Omega$ for positive linear combinations $S$ of probabilities of events, $S \leq \Omega$. Exclusive events in $S$ can be represented as adjacent vertices of a graph called the exclusivity graph of $S$. In the case that events correspond to the outcomes of quantum projective measurements, quantum probabilities are intimately related to the Gr\"otschel-Lov\'asz-Schrijver theta body of the exclusivity graph. Then, one can easily compute an upper bound to the maximum quantum violation of any NC or Bell inequality by optimizing $S$ over the theta body and calculating the Lov\'asz number of the corresponding exclusivity graph. In some cases, this upper bound is tight and gives the exact maximum quantum violation. However, in general, this is not the case. The reason is that the exclusivity graph does not distinguish among the different ways exclusivity can occur in Bell-inequality (and similar) scenarios. An interesting question is whether there is a graph-theoretical concept which accounts for this problem. Here we show that, for any given $N$-partite Bell inequality, an edge-coloured multigraph composed of $N$ single-colour graphs can be used to encode the relationships of exclusivity between each party's parts of the events. Then, the maximum quantum violation of the Bell inequality is exactly given by a refinement of the Lov\'asz number that applies to these edge-coloured multigraphs. We show how to calculate upper bounds for this number using a hierarchy of semi-definite programs and calculate upper bounds for $I_3$, $I_{3322}$ and the three bipartite Bell inequalities whose exclusivity graph is a pentagon. The multigraph-theoretical approach introduced here may remove some obstacles in the program of explaining quantum correlations from first principles., Comment: 21 pages, 5 figures