arXiv subjects

A. C. S. Costa

Publications and source records attributed to A. C. S. Costa.

10 recordsLinked to original sources

arXiv2026

The Thermodynamic Geometry of Conditional Control

Information is widely regarded as the resource underlying the thermodynamic advantages enabled by conditional control. We show, however, that informational quantities such as Holevo information and accessible distinguishability, although constraining the achievable advantage, do not uniquely determine its thermodynamic value. The missing ingredient is a passive spectral rearrangement vector that characterizes the effect of conditioning on the ensemble. Specifically, the conditional-control advantage is exactly determined by the geometric pairing between this vector and the Hamiltonian energy-gap structure. This result reveals a thermodynamic geometry of conditional control, explains how informationally equivalent ensembles can possess different thermodynamic values, and identifies the passive spectral rearrangement vector as the minimal operational descriptor required to determine the thermodynamic value of conditional control for a fixed Hamiltonian.

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arXiv2026

Quantum Crossovers Revealed by Local Measurements

Quantum crossover phenomena play a central role in few-body open quantum systems, yet their identification often relies on global or model-dependent indicators. In this work, we demonstrate that crossovers can be robustly characterized through purely local measurements, establishing a direct connection between local quantum Fisher information and the onset of crossover behavior. We further demonstrate that quantum obesity does not, in general, generalize the quantum steering ellipsoid volume as a universal indicator of crossover. Instead, we identify regimes in which the ellipsoid volume remains insensitive to the transition, while the relevant signatures are encoded in the behavior of the local Bloch vector. These results reveal a geometric distinction between local and global indicators of crossovers.

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arXiv2024

Analysis of Quantum Steering Measures

The effect of quantum steering describes a possible action at a distance via local measurements. In the last few years, several criteria have been proposed to detect this type of correlation in quantum systems. However, there are few approaches presented in order to measure the degree of steerability of a given system. In this work, we are interested in investigating possible ways to quantify quantum steering, where we based our analysis on different criteria presented in the literature.

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arXiv2021

Quantum resources of the steady-state of three coupled qubits: Microscopic versus Phenomenological model

Quantum resources, such as entanglement, steering, and Bell nonlocality, are evaluated for three coupled qubits in the steady-state configuration. We employ the phenomenological master equation and the microscopic master equation to probe such quantum resources, which provide very different results depending on the system configuration. In particular, steering and Bell nonlocality are null within the phenomenological model, while they reach considerable values within the microscopic model. These results show that the phenomenological approach is not able to capture all quantum resources of the system. We also provide an analytical expression for the steady-state and quantum resources of the system composed of three coupled qubits in the zero temperature limit. Such results demonstrate that quantum resources between two qubits are strongly affected by the third qubit in a nontrivial way.

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arXiv2020

Information-based approach towards a unified resource theory

Resource theories play an important role in quantum information theory, as they identify resourceful states and channels that are potentially useful for the accomplishment of tasks that would be otherwise unreachable. The elementary structure of such theories, which is based on the definition of free states and free operations, successfully accommodates different nonclassical aspects, such as quantum coherence and entanglement, but it is still not clear whether and how far such formal framework can be extended. In this work, by taking information as the most primitive quantum resource and defining resource-destroying operations, we develop a unifying approach that proves able to encompass several nonclassical aspects, including the newly developed concepts of quantum irreality and realism-based nonlocality.

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arXiv2016

System-environment correlations for dephasing two-qubit states coupled to thermal baths

Based on the exact dynamics of a two-qubit system and environment, we investigate system-environment (SE) quantum and classical correlations. The coupling is chosen to represent a dephasing channel for one of the qubits and the environment is a proper thermal bath. First we discuss the general issue of dilation for qubit phase damping. Based on the usual thermal bath of harmonic oscillators, we derive criteria of separability and entanglement between an initial $X$ state and the environment. Applying these criteria to initial Werner states, we find that entanglement between the system and environment is built up in time for temperatures below a certain critical temperature $T_{\mathrm{crit}}$. On the other hand, the total state remains separable during those short times that are relevant for decoherence and loss of entanglement in the two-qubit state. Close to $T_{\mathrm{crit}}$ the SE correlations oscillate between separable and entangled. Even though these oscillations are also observed in the entanglement between the two qubits, no simple relation between the loss of entanglement in the two-qubit system and the build-up of entanglement between the system and environment is found.

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arXiv2016

Generalized discord, entanglement, Einstein-Podolsky-Rosen steering, and Bell nonlocality in two-qubit systems under (non-)Markovian channels: Hierarchy of quantum resources and chronology of deaths and births

Generalized quantum discord $(D_q)$, Einstein-Podolsky-Rosen steering $(S)$, entanglement $(E)$, and Bell nonlocality ($N$), are logically distinct quantifiers of quantum correlations. All these measures capture nonclassical aspects of quantum states and play some role as resources in quantum information processing. In this work, we look for the hierarchy satisfied by these quantum correlation witnesses for a class of two-qubit states. We show that $N \triangleright S\triangleright E\triangleright D_q$, meaning that nonlocality implies steering, which in turn implies entanglement, which then implies $q$-discord. For the quantum states under concern, we show that the invariance of this hierarchy under noisy quantum channels directly implies a death chronology. Additionally, we have found that sudden death of all quantum resources except discord is absent only for a subset of states of measure zero. At last, we provide an illustration of another consequence of the aforementioned hierarchy, namely, the existence of a sudden birth chronology under non-Markovian channels.

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arXiv2016

Quantification of Einstein-Podolski-Rosen steering for two-qubit states

In the last few years, several criteria to identify Eistein-Podolski-Rosen steering have been proposed and experimentally implemented. On the operational side, however, the evaluation of the steerability degree of a given state has shown to be a difficult task and only a few results are known. In this work, we propose a measure of steering that is based on the maximal violation of well established steering inequalities. Applying this approach to two-qubit states, we managed to derive simple closed formulas for steering in the two- and three-measurement scenarios. Among the options investigated, a measure has been found that correctly satisfies the entanglement-steering-nonlocality hierarchy and reproduces results reported so far.

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arXiv2014

Monogamy and backflow of mutual information in non-Markovian thermal baths

We investigate the dynamics of information among the parties of tripartite systems. We start by proving two results concerning the monogamy of mutual information. The first one states that mutual information is monogamous for generic tripartite pure states. The second shows that in general mutual information is monogamous only if the amount of genuine tripartite correlations is large enough. Then, we analyze the internal dynamics of tripartite systems whose parties do not exchange energy. In particular, we allow for one of the subsystems to play the role of a finite thermal bath. As a result, we find a typical scenario in which local information tends to be converted into delocalized information. Moreover, we show that (i) the information flow is reversible for finite thermal baths at low temperatures, (ii) monogamy of mutual information is respected throughout the dynamics, and (iii) genuine tripartite correlations are typically present. Finally, we analytically calculate a quantity capable of revealing favorable regimes for non-Markovianity in our model.

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arXiv2013

Bayes' rule, generalized discord, and nonextensive thermodynamics

Generalized measures of quantum correlations are derived by taking Bayes' rule as the only fundamental principle. The resulting quantifiers satisfy several desirable conditions for a measure of quantum correlations and are shown to admit operational interpretation in terms of the difference in efficiency of quantum and classical demons in allowing for the extraction of generalized work from a heat bath. The link with discord is established by adopting the $q$ entropy as entropic principle. This allows us to reproduce, within a one-parameter formalism, both the entropic and the geometric measures of discord and physically distinguish them within the context of the nonextensive thermodynamics. Besides offering a unified view of several measures of correlations in terms of the Bayesian principle and its connection with thermodynamics, our approach unveils a bridge to the nonextensive statistical mechanics.

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