arXiv subjects

Marcelo Terra Cunha

Publications and source records attributed to Marcelo Terra Cunha.

At least 19 recordsLinked to original sources

arXiv2026

How Quantum Contextuality disappears in the Classical Limit

The emergence of classicality is fundamentally driven by the interaction between a quantum system and its environment. Foundational open-system approaches, notably the Caldeira-Leggett model, successfully captured how these interactions lead to macroscopic effects like quantum dissipation and decoherence. However, these approaches often leave the precise definitions of classicality and quantumness ambiguous. In quantum information theory, this boundary is a heavily scrutinized question, and Kochen-Specker contextuality emerges as a hallmark of nonclassicality. It is therefore natural to investigate whether decoherence can actually suppress this property. Taking this path creates an apparent conundrum, once there exist two distinct manifestations of quantum contextuality: state-dependent and state-independent ones. While state-dependent contextuality naturally vanishes under state degradation, state-independent contextuality could persist for any quantum state, since it shows up even for the maximally mixed state! In this paper, we resolve this apparent paradox by analyzing sequential measurement implementations of the paradigmatic Klyachko, Can, Binicioğlu, and Shumovsky (KCBS) and Peres-Mermin prepare-and-measure scenarios under the influence of depolarizing channels. By introducing noise both prior to and in between measurements, and by analyzing the resulting sequential correlators in both the Schrödinger and Heisenberg pictures, we show how open-system dynamics suppress the correlations required to witness contextuality, leading to classicalization.

quant-ph↗

arXiv2026

Unexpected consequences of Post-Quantum theories in the graph-theoretical approach to correlations

This work explores the implications of the exclusivity principle (EP) in the context of quantum and postquantum correlations. We first establish a key technical result demonstrating that given the set of correlations for a complementary experiment, the EP restricts the maximum set of correlations for the original experiment to the antiblocking set. Based on it, we can prove our central result: if all quantum behaviors are accessible in Nature, the EP guarantees that no postquantum behaviors can be realized. This can be seen as a generalization of the result of B. Amaral et al. [Phys. Rev. A 89, 030101(R) (2014)], to a wider range of scenarios. It also provides novel insights into the structure of quantum correlations and their limitations.

quant-ph↗

arXiv2026

Cartan-Khaneja-Glaser decomposition of $SU(2^n)$ via involutive automorphisms

We present a novel algorithm for performing the Cartan-Khaneja-Glaser decomposition of unitary matrices in $SU(2^n)$, a critical task for efficient quantum circuit design. Building upon the approach introduced by Sá Earp and Pachos (2005), we overcome key limitations of their method, such as reliance on ill-defined matrix logarithms and the convergence issues of truncated Baker-Campbell-Hausdorff(BCH) series. Our reformulation leverages the algebraic structure of involutive automorphisms and symmetric Lie algebra decompositions to yield a stable and recursive factorization process. We provide a full Python implementation of the algorithm, available in an open-source repository, and validate its performance on matrices in $SU(8)$ and $SU(16)$ using random unitary benchmarks. The algorithm produces decompositions that are directly suited to practical quantum hardware, with factors that can be implemented near-optimally using standard gate sets.

quant-ph↗

arXiv2024

Trade-off relations between Bell nonlocality and local Kochen-Specker contextuality in generalized Bell scenarios

The relations between Bell nonlocality and Kochen-Specker contextuality have been subject of research from many different perspectives in the last decades. Recently, some interesting results on these relations have been explored in the so-called generalized Bell scenarios, that is, scenarios where Bell spatial separation (or agency independence) coexist with (at least one of the) parties' ability to perform compatible measurements at each round of the experiment. When this party has an $n$-cycle compatiblity setup, it was first claimed that Bell nonlocality could not be concomitantly observed with contextuality at this party's local experiment. However, by a more natural reading of the definition of locality, it turns out that both Bell nonlocality and local contextuality can, in fact, be jointly present. In spite of it, in this work we prove that there cannot be arbitrary amounts of both of these two resources together. That is, we show the existence of a trade-off relation between Bell nonlocality and local contextuality in such scenarios. We explore this trade-off both in terms of inequalities and quantifiers, and we discuss how it can be understood in terms of a `global' notion of contextuality. Furthermore, we show that such notion does not only encompass local contextuality and Bell nonlocality, but also other forms of nonclassical correlations.

quant-ph↗

arXiv2024

Characterizing Optimal-speed unitary time evolution of pure and quasi-pure quantum states

We present a characterization of the Hamiltonians that generate optimal-speed unitary time evolution and the associated dynamical trajectory, where the initial states are either pure states or quasi-pure quantum states. We construct the manifold of pure states as an orbit under the conjugation action of the Lie group $\SU(n)$ on the manifold of one-dimensional orthogonal projectors, obtaining an isometry with the flag manifold $\SU(n)/\textnormal{S}(\textnormal{U}(1)\times \textnormal{U}(n-1 ))$. From this construction, we show that Hamiltonians generating optimal-speed time evolution are fully characterized by equigeodesic vectors of $\SU(n)/\textnormal{S}(\textnormal{U}(1)\times \textnormal{U}(n-1))$. We later extend that result to quasi-pure quantum states.

quant-ph↗

arXiv2024

The quantum maxima for the basic graphs of exclusivity are not reachable in Bell scenarios

A necessary condition for the probabilities of a set of events to exhibit Bell nonlocality or Kochen-Specker contextuality is that the graph of exclusivity of the events contains induced odd cycles with five or more vertices, called odd holes, or their complements, called odd antiholes. From this perspective, events whose graph of exclusivity are odd holes or antiholes are the building blocks of contextuality. For any odd hole or antihole, any assignment of probabilities allowed by quantum mechanics can be achieved in specific contextuality scenarios. However, here we prove that, for any odd hole, the probabilities that attain the quantum maxima cannot be achieved in Bell scenarios. We also prove it for the simplest odd antiholes. This leads us to the conjecture that the quantum maxima for any of the building blocks cannot be achieved in Bell scenarios. This result sheds light on why the problem of whether a probability assignment is quantum is decidable, while whether a probability assignment within a given Bell scenario is quantum is, in general, undecidable. This also helps to undertand why identifying principles for quantum correlations is simpler when we start by identifying principles for quantum sets of probabilities defined with no reference to specific scenarios.

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arXiv2023

Can multiple observers detect KS-contextuality?

KS-contextuality is a crucial feature of quantum theory. Previous research demonstrated the vanishing of $N$-cycle KS-contextuality in setups where multiple independent observers measure sequentially on the same system, which we call Public Systems. This phenomenon can be explained as the additional observers' measurements degrading the state and depleting the quantum resource. This explanation would imply that state-independent contextuality should survive in such a system. In this paper, we show that this is not the case. We achieved this result by simulating an observer trying to violate the Peres-Mermin noncontextuality inequality in a Public System. Additionally, we provide an analytical description of our setup, explaining the loss of contextuality even in the state-independent case. Ultimately, these results show that state-independent contextuality is not independent of what happens to the system in-between the measurements of a context.

quant-ph↗

arXiv2023

Generalized Bell scenarios: disturbing consequences on local-hidden-variable models

Bell nonlocality and Kochen-Specker contextuality are among the main topics of foundations of quantum theory. Both of them are related to stronger-than-classical correlations, with the former usually referring to spatially separated systems while the latter considering a single system. In recent works, a unified framework for these phenomena was presented. This article reviews, expands and obtains new results regarding this framework. Contextual and disturbing features inside the local models are explored, which allows for the definition of different local sets with a non-trivial relation among them. The relations between the set of quantum correlations and these local sets are also considered, and post-quantum local behaviours are found. Moreover, examples of correlations that are both local and non-contextual but such that these two classical features cannot be expressed by the same hidden variable model are shown. Extensions of the Fine-Abramsky-Brandenburger theorem are also discussed.

quant-ph↗

arXiv2023

Quantum sets of the multicolored-graph approach to contextuality

The CHSH inequalities are the most famous examples of Bell inequalities. Cabello, Severini, and Winter (CSW) came up with a graph approach to noncontextuality inequalities, which connects some graph-theoretic concepts to quantum and classical correlations. For example, the theta body of the exclusivity graph can be associated with the set of correlations achieved by quantum theory. Following the CSW approach, one may think that the theta body of the CHSH graph, is equal to the quantum set of the CHSH Bell inequality, but is this really true? All assumptions about the CHSH inequalities come from Bell scenarios, while CSW approach only demands the exclusivity structure of a non-contextuality (NC) scenario. To deal with the extra structure related to the presence of different players in a Bell scenario like CHSH, the colored-graph approach was introduced. Does it make any difference to think about CHSH as a Bell scenario or a more general NC scenario? The Bell CHSH inequality is represented by a bicolored graph and the NC CHSH inequality by a simple graph, which is the shadow of the colored graph. In general, we have that the theta body of the colored graph is a subset of the theta body of its shadow graph in the same way that the Lovàsz number, which corresponds to the quantum bound, of the simple graph is greater than or equal to the Lovàsz number of the colored graph. In the case of the CHSH inequality, we have that the Lovàsz numbers are equal. Does this accident also hold for the corresponding quantum sets? Is it true that the theta bodies are equal, which would mean that every correlation reached by quantum theory applied to the CHSH NC scenario could also be obtained at the in principle more restrictive CHSH Bell scenario? In this paper our answer to such a question is negativ. This implies that there are quantum correlations which can not be obtained under Bell restrictions.

quant-ph↗

arXiv2022

Synchronous observation of Bell nonlocality and state-dependent Kochen-Specker contextuality

Bell nonlocality and Kochen-Specker contextuality are two remarkable nonclassical features of quantum theory, related to strong correlations between outcomes of measurements performed on quantum systems. Both phenomena can be witnessed by the violation of certain inequalities, the simplest and most important of which are the Clauser-Horne-Shimony-Holt (CHSH) and the Klyachko-Can-Binicioǧlu-Shumovski (KCBS), for Bell nonlocality and Kochen-Specker contextuality, respectively. It has been shown that, using the most common interpretation of Bell scenarios, quantum systems cannot violate both inequalities concomitantly, thus suggesting a monogamous relation between the two phenomena. In this Letter, we show that the joint consideration of the CHSH and KCBS inequalities naturally calls for the so-called generalized Bell scenarios, which, contrary to the previous results, allows for joint violation of them. A photonic experiment thus tests the synchronous violation of both CHSH and KCBS inequalities. Our results agree with the theoretical predictions, thereby providing experimental proof of the coexistence of Bell nonlocality and Kochen-Specker contextuality in the simplest scenario, and shed new light for further explorations of nonclassical features of quantum systems.

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arXiv2021

Emergence of noncontextuality under quantum Darwinism

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 Brandão, 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.

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arXiv2020

Investigating Coarse-Grainings and Emergent Quantum Dynamics with Four Mathematical Perspectives

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.

quant-ph↗

arXiv2020

Classical Limits and Contextuality in a Scenario of Multiple Observers

Contextuality is regarded as a non-classical feature, challenging our everyday intuition; quantum contextuality is currently seen as a resource for many applications in quantum computation, being responsible for quantum advantage over classical analogs. In our work, we adapt the $N$-cycle scenarios with odd $N$ to multiple independent observers which measure the system sequentially. We analyze the possibility of violating the inequalities as a function of the number of observers and under different measurement protocols. We then reinterpret the results as an open quantum system where the environment is divided into fragments. In this context, the results show the emergence of non-contextuality in such a setting, bringing together the quantum behavior to our classical experience. We then compare such emergence of non-contextuality with that of objectivity under the `Environment as a Witness paradigm'.

quant-ph↗

arXiv2020

Bell Non-Locality in Many Body Quantum Systems with Exponential Decay of Correlations

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.

quant-ph↗

arXiv2019

Uniqueness of the joint measurement and the structure of the set of compatible quantum measurements

We address the problem of characterising the compatible tuples of measurements that admit a unique joint measurement. We derive a uniqueness criterion based on the method of perturbations and apply it to show that extremal points of the set of compatible tuples admit a unique joint measurement, while all tuples that admit a unique joint measurement lie in the boundary of such a set. We also provide counter-examples showing that none of these properties are both necessary and sufficient, thus completely describing the relation between joint measurement uniqueness and the structure of the compatible set. As a by-product of our investigations, we completely characterise the extremal and boundary points of the set of general tuples of measurements and of the subset of compatible tuples.

quant-ph↗

arXiv2019

Measurement compatibility in Bell nonlocality tests

Incompatibility of observables, or measurements, is one of the key features of quantum mechanics, related, among other concepts, to Heisenberg's uncertainty relations and Bell nonlocality. In this manuscript we show, however, that even though incompatible measurements are necessary for the violation of any Bell inequality, some relevant Bell-like inequalities may be obtained if compatibility relations are assumed between the local measurements of one (or more) of the parties. Hence, compatibility of measurements is not necessarily a drawback and may, however, be useful for the detection of Bell nonlocality and device-independent certification of entanglement.

quant-ph↗

arXiv2019

On Measures and Measurements: a Fibre Bundle approach to Contextuality

Contextuality is the failure of "local" probabilistic models to become global ones. In this paper we introduce the notions of \emph{measurable fibre bundles}, \emph{probability fibre bundles}, and \emph{sample fibre bundle} which capture and make precise the former statement. The central notions of contextuality are discussed under this formalism, examples worked out, and some new aspects pointed out.

math.PR↗

arXiv2019

Quantifying quantum invasiveness

We propose a resource theory of the quantum invasiveness of general quantum operations, i.e., those defined by quantum channels in Leggett-Garg scenarios. We are then able to compare the resource-theoretic framework of quantum invasiveness to the resource theory of coherence. We also show that the Fisher information is a quantifier of quantum invasiveness. This result allows us to establish a direct connection between the concept of quantum invasiveness and quantum metrology, by exploring the utility of the definition of quantum invasiveness in the context of metrological protocols.

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