arXiv subjects

Ismael L. Paiva

Publications and source records attributed to Ismael L. Paiva.

At least 19 recordsLinked to original sources

arXiv2026

Networks of quantum reference frames and the nature of conserved quantities

We show that networks of quantum frames of reference, in which one frame may be used to produce multiple other frames that in their turn prepare systems which may interact with one another, have counterintuitive properties that make following the exchange of conserved quantities very subtle, and raise questions about the very nature of conserved quantities. In addition, we present an alternative approach to analysing quantum reference frames that we believe will be useful in discussions related to quantum frames of reference.

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arXiv2024

Unveiling quantum complementarity tradeoffs in relativistic scenarios

Complementarity plays a pivotal role in understanding a diverse range of quantum phenomena. Here, we show how the tradeoff between quantities of a complete complementarity relation is modified in an arbitrary spacetime for a particle with an internal spin. This effect stems from local Wigner rotations in the spacetime, which couple the spin to the system's external degrees of freedom. To conduct our study, we utilize two generalized delayed-choice interferometers. Despite differences in complementarity tradeoffs inside the interferometers, the interferometric visibility of both setups coincides in any relativistic regime. Our results extend the finding that general relativity induces a universal decoherence effect on quantum superpositions, as local Wigner rotations, being purely kinematical, preclude any spin dynamics. To illustrate, we analyze the Newtonian limit of our results.

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arXiv2024

Quantum switch instabilities with an open control

The superposition of causal order shows promise in various quantum technologies. However, the fragility of quantum systems arising from environmental interactions, leading to dissipative behavior and irreversibility, demands a deeper understanding of the possible instabilities in the coherent control of causal orders. In this work, we employ a collisional model to investigate the impact of an open control system on the generation of interference between two causal orders. We present the environmental instabilities for the switch of two arbitrary quantum operations and examine the influence of environmental temperature on each potential outcome of control post-selection. Additionally, we explore how environmental instabilities affect protocol performance, including switching between mutually unbiased measurement observables and refrigeration powered by causal order superposition, providing insights into broader implications.

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arXiv2024

Geometric phases and the Sagnac effect: Foundational aspects and sensing applications

Geometric phase is a key player in many areas of quantum science and technology. In this review article, several foundational aspects of quantum geometric phases and their relations to classical geometric phases are outlined. How the Aharonov--Bohm and Sagnac effects fit into this context is then discussed. Moreover, a concise overview of technological applications of the latter, with special emphasis on gravitational sensing, like in gyroscopes and gravitational wave detectors is presented.

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arXiv2024

Induced on-demand revival in coined quantum walks on infinite $d$-dimensional lattices

The study of recurrences and revivals in quantum systems has attracted a great deal of interest because of its importance in the control of quantum systems and its potential use in developing new technologies. In this work, we introduce a protocol to induce full-state revivals in a huge class of quantum walks on a $d$-dimensional lattice governed by a $c$-dimensional coin system. The protocol requires two repeated interventions in the coin degree of freedom. We also present a characterization of the walks that admits such a protocol. Moreover, we modify the quantity known as Pólya number, typically used in the study of recurrences in classical random walks and quantum walks, to create a witness of the first revival of the walk.

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arXiv2024

Nonrelativistic spatiotemporal quantum reference frames

Quantum reference frames have attracted renewed interest recently, as their exploration is relevant and instructive in many areas of quantum theory. Among the different types, position and time reference frames have captivated special attention. Here, we introduce and analyze a nonrelativistic framework in which each system contains an internal clock, in addition to its external (spatial) degree of freedom and, hence, can be used as a spatiotemporal quantum reference frame. We present expressions for expectation values and variances of relevant observables in different perspectives, as well as relations between these quantities in different perspectives in scenarios with no interactions. In particular, we show that even in these simple scenarios, the relative uncertainty between clocks affects the relative spatial spread of the systems.

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arXiv2023

Quantum circuits for measuring weak values, Kirkwood--Dirac quasiprobability distributions, and state spectra

Weak values and Kirkwood--Dirac (KD) quasiprobability distributions have been independently associated with both foundational issues in quantum theory and advantages in quantum metrology. We propose simple quantum circuits to measure weak values, KD distributions, and spectra of density matrices without the need for post-selection. This is achieved by measuring unitary-invariant, relational properties of quantum states, which are functions of Bargmann invariants, the concept that underpins our unified perspective. Our circuits also enable experimental implementation of various functions of KD distributions, such as out-of-time-ordered correlators (OTOCs) and the quantum Fisher information in post-selected parameter estimation, among others. An upshot is a unified view of nonclassicality in all those tasks. In particular, we discuss how negativity and imaginarity of Bargmann invariants relate to set coherence.

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arXiv2023

Aharonov-Bohm effect with an effective complex-valued vector potential

The interaction between a quantum charge and a dynamic source of a magnetic field is considered in the Aharonov-Bohm scenario. It is shown that, in weak interactions with a post-selection of the source, the effective vector potential is, generally, complex-valued. This leads to new experimental protocols to detect the Aharonov-Bohm phase before the source is fully encircled. While this does not necessarily change the nonlocal status of the Aharonov-Bohm effect, it brings new insights into it. Moreover, we discuss how these results might have consequences for the correspondence principle, making complex vector potentials relevant to the study of classical systems.

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arXiv2023

Coherence and realism in the Aharonov-Bohm effect

The Aharonov-Bohm effect is a fundamental topological phenomenon with a wide range of applications. It consists of a charge encircling a region with a magnetic flux in a superposition of wave packets having their relative phase affected by the flux. In this work, we analyze this effect using an entropic measure known as realism, originally introduced as a quantifier of a system's degree of reality and mathematically related to notions of global and local quantum coherence. More precisely, we look for observables that lead to gauge-invariant realism associated with the charge before it completes its loop. We find that the realism of these operators has a sudden change when the line connecting the center of both wave packets crosses the solenoid. Moreover, we consider the case of a quantized magnetic-field source, pointing out similarities and differences between the two cases. Finally, we discuss some consequences of these results.

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arXiv2023

Time-symmetry and topology of the Aharonov-Bohm effect

The Aharonov-Bohm (AB) effect has been highly influential in fundamental and applied physics. Its topological nature commonly implies that an electron encircling a magnetic flux source in a field-free region must close the loop in order to generate an observable effect. In this Letter, we study a variant of the AB effect that apparently challenges this concept. The significance of weak values and nonlocal equations of motion is discussed as part of the analysis, shedding light on and connecting all these fundamental concepts.

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arXiv2022

Non-inertial quantum clock frames lead to non-Hermitian dynamics

The operational approach to time is a cornerstone of relativistic theories, as evidenced by the notion of proper time. In standard quantum mechanics, however, time is an external parameter. Recently, many attempts have been made to extend the notion of proper time to quantum mechanics within a relational framework. Here, we use similar ideas combined with the relativistic mass-energy equivalence to study an accelerating massive quantum particle with an internal clock system. We show that the ensuing evolution from the perspective of the particle's internal clock is non-Hermitian. This result does not rely on specific implementations of the clock. As a particular consequence, we prove that the effective Hamiltonian of two gravitationally interacting particles is non-Hermitian from the perspective of the clock of either particle.

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arXiv2022

Dynamical nonlocality in quantum time via modular operators

We formalize the concept of the modular energy operator within the Page and Wootters timeless framework. As a result, this operator is elevated to the same status as the more studied modular operators of position and momentum. In analogy with dynamical nonlocality in space associated with the modular momentum, we introduce and analyze the nonlocality in time associated with the modular energy operator. Some applications of our formalization are provided through illustrative examples.

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arXiv2022

Flow of time during energy measurements and the resulting time-energy uncertainty relations

Uncertainty relations play a crucial role in quantum mechanics. Well-defined methods exist for the derivation of such uncertainties for pairs of observables. Other approaches also allow the formulation of time-energy uncertainty relations, even though time is not an operator in standard quantum mechanics. However, in these cases, different approaches are associated with different meanings and interpretations for these relations. The one of interest here revolves around the idea of whether quantum mechanics inherently imposes a fundamental minimum duration for energy measurements with a certain precision. In our study, we investigate within the Page and Wootters timeless framework how energy measurements modify the relative "flow of time" between internal and external clocks. This provides a unified framework for discussing the subject, allowing us to recover previous results and derive new ones. In particular, we show that the duration of an energy measurement carried out by an external system cannot be performed arbitrarily fast from the perspective of the internal clock. Moreover, we show that during any energy measurement the evolution given by the internal clock is non-unitary.

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arXiv2021

Quantum logical entropy: fundamentals and general properties

Logical entropy gives a measure, in the sense of measure theory, of the distinctions of a given partition of a set, an idea that can be naturally generalized to classical probability distributions. Here, we analyze how fundamental concepts of this entropy and other related definitions can be applied to the study of quantum systems, leading to the introduction of the quantum logical entropy. Moreover, we prove several properties of this entropy for generic density matrices that may be relevant to various areas of quantum mechanics and quantum information. Furthermore, we extend the notion of quantum logical entropy to post-selected systems.

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arXiv2020

On the extension of positive definite kernels to topological algebras

We define an extension of operator-valued positive definite functions from the real or complex setting to topological algebras, and describe their associated reproducing kernel spaces. The case of entire functions is of special interest, and we give a precise meaning to some power series expansions of analytic functions that appears in many algebras.

math.FA↗

arXiv2020

Magnetic forces in the absence of a classical magnetic field

It is shown that, in some cases, the effect of discrete distributions of flux lines in quantum mechanics can be associated with the effect of continuous distributions of magnetic fields with special symmetries. In particular, flux lines with an arbitrary value of magnetic flux can be used to create energetic barriers, which can be used to confine quantum systems in specially designed configurations. This generalizes a previous work where such energy barriers arose from flux lines with half-integer fluxons. Furthermore, it is shown how the Landau levels can be obtained from a two-dimensional grid of flux lines. These results suggest that the classical magnetic force can be seen as emerging entirely from the Aharonov-Bohm effect. Finally, the basic elements of a semi-classical theory that models the emergence of classical magnetic forces from fields with special symmetries are introduced.

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arXiv2019

Topological bound states for quantum charges

We discuss how, in appropriately designed configurations, solenoids carrying a semifluxon can be used as topological energy barriers for charged quantum systems. We interpret this phenomenon as a consequence of the fact that such solenoids induce nodal lines in the wave function describing the charge, which on itself is a consequence of the Aharonov-Bohm effect. Moreover, we present a thought experiment with a cavity where two solenoids are sufficient to create bound states.

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arXiv2018

A general setting for functions of Fueter variables: differentiability, rational functions, Fock module and related topics

We develop some aspects of the theory of hyperholomorphic functions whose values are taken in a Banach algebra over a field -- assumed to be the real or the complex numbers -- and which contains the field. Notably, we consider Fueter expansions, Gleason's problem, the theory of hyperholomorphic rational functions, modules of Fueter series, and related problems. Such a framework includes many familiar algebras as particular cases. The quaternions, the split quaternions, the Clifford algebras, the ternary algebra, and the Grassmann algebra are a few examples of them.

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