arXiv subjects

Nadja K. Bernardes

Publications and source records attributed to Nadja K. Bernardes.

At least 19 recordsLinked to original sources

arXiv2026

Effective Transition from Weak to Essential Non-Markovianity Induced by Coarse-Graining

Quantum channels generally reduce the distinguishability of quantum states, thereby constraining information transmission and processing in open quantum systems. While it is known that distinguishability can be partially recovered through suitable post-processing protocols, a systematic characterization of the maximal achievable gain has remained elusive. Here, we establish a general framework to determine and optimize the recovery of distinguishability induced by a quantum channel. We introduce an algorithm that identifies the optimal implementation of a multi-copy coarse-graining protocol applicable to arbitrary channels. Within this framework, we derive a general upper bound on the attainable distinguishability gain and quantify the performance of the protocol through its tightness relative to this bound. Our results show that collective coarse-graining can lead to effective dynamics exhibiting the operational signatures of essential non-Markovianity even when the underlying microscopic dynamics remain weakly non-Markovian. A detailed analysis reveals a nontrivial trade-off between mathematical optimality (bound saturation) and operational optimality, together with a strong dependence on both the input ensemble and the number of copies. Taken together, these findings provide a unified and quantitative framework to assess, optimize, and interpret distinguishability recovery in open quantum systems while showing how collective processing can qualitatively modify the operational memory properties of effective dynamical descriptions.

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arXiv2026

State Preparation Protocols for Entangled States via Open Quantum Walks

Open quantum walks couple transitions on a graph to quantum operations on an internal degree of freedom. We use this structure to formulate protocols for quantum state preparation with nonunitary Kraus operators. We construct a ring-shaped OQW preparing an ensemble of Dicke states, with W states appearing as the single-excitation case, from which any individual Dicke state is recovered by postselecting the walker position; its convergence is governed by the spectral gap of the underlying Markov chain, for which we obtain a closed-form approximate expression. For GHZ states we present a two-node protocol using Kraus operators built from projective measurements that prepares them deterministically without requiring a measurement of the walker, and analyze how unsharp measurements affect the results and the convergence of the walk. We also show that the quantum trajectories method embeds naturally in the OQW framework as a graph-structured collision model.

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arXiv2026

Realizing the Petz Recovery Map on an NMR Quantum Processor

The Petz recovery map is a central construct in quantum information theory, providing an explicit, channel-aware prescription for reversing the effects of noise. Unlike standard quantum operations, the Petz map is intrinsically dependent on a chosen reference state, which makes its physical implementation and experimental validation particularly challenging. Here, we report an experimental realization of Petz recovery maps on a nuclear magnetic resonance (NMR) quantum processor using the duality quantum computing (DQC) algorithm. We investigate two paradigmatic single-qubit noise models: amplitude damping and phase damping, and construct corresponding families of Petz recovery maps for varying reference states. By systematically tuning the reference state, we experimentally demonstrate the state-adapted nature of Petz recovery, observing both enhanced recovery when the reference state is well matched and fidelity degradation for mismatched choices. Our experimental results show close quantitative agreement with theoretical predictions, providing direct evidence that the Petz recovery map constitutes a physically realizable, reference-state-dependent recovery channel rather than a purely formal inverse of noise. This work bridges the gap between the abstract information-theoretic formulation of Petz recovery and its implementation on a realistic quantum platform, and establishes an experimental benchmark for testing noise-adapted recovery strategies on near-term quantum devices.

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arXiv2026

Dissipative realization of a quantum distance-based classifier using open quantum walks

Open quantum walks (OQWs) constitute a class of quantum walks whose dynamics are entirely driven by interactions with the environment. It is well known that OQWs provide a general framework for implementing dissipative quantum computation. In this work, we demonstrate the feasibility of running the previously proposed quantum distance-based classifier within the open quantum walk computation model, and we show that its expected runtime remains finite even in the slower regime.

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arXiv2025

Dynamics and computation in linear open quantum walks

Open Quantum Walks (OQW) are a type of quantum walk governed by the system's interaction with its environment. We explore the time evolution and the limit behavior of the OQW framework for Quantum Computation and show how we can represent random unitary quantum channels, such as the dephasing and depolarizing channels, in this model. We also develop a simulation protocol with circuit representation for this model, which is heavily inspired by the fact that graphs represent OQW and are, thereby, local (meaning that the state in a particular node interacts only with its neighborhood). We obtain asymptotic advantages in the system's dimension, circuit depth, and CNOT count compared to other simulation methods.

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arXiv2025

Efficient and operational quantifier of non-divisibility in terms of channel discrimination

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.

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arXiv2025

Divide-and-Conquer Simulation of Open Quantum Systems

One of the promises of quantum computing is to simulate physical systems efficiently. However, the simulation of open quantum systems - where interactions with the environment play a crucial role - remains challenging for quantum computing, as it is impossible to implement deterministically non-unitary operators on a quantum computer without auxiliary qubits. The Stinespring dilation can simulate an open dynamic but requires a high circuit depth, which is impractical for NISQ devices. An alternative approach is parallel probabilistic block-encoding methods, such as the Sz.-Nagy and Singular Value Decomposition dilations. These methods result in shallower circuits but are hybrid methods, and we do not simulate the quantum dynamic on the quantum computer. In this work, we describe a divide-and-conquer strategy for preparing mixed states to combine the output of each Kraus operator dilation and obtain the complete dynamic on quantum hardware with a lower circuit depth. The work also introduces a balanced strategy that groups the original Kraus operators into an expanded operator, leading to a trade-off between circuit depth, CNOT count, and number of qubits. We perform a computational analysis to demonstrate the advantages of the new method and present a proof-of-concept simulation of the Fenna-Matthews-Olson dynamic on current quantum hardware.

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arXiv2024

Non-Markovian to Markovian decay in structured environments with correlated disorder

Manipulating the dynamics of open quantum systems is a crucial requirement for large-scale quantum computers. Finding ways to overcome or extend decoherence times is a challenging task. Already at the level of a single two-level atom, its reduced dynamics with respect to a larger environment can be very complex. Structured environments, for instance, can lead to various regimes other than memoryless Markovian spontaneous emission. Here, we consider an atom coupled to an array of coupled cavities in the presence of on-site correlated disorder. The correlation is long-ranged and associated with the trace of a fractional Brownian motion following a power-law spectrum. With the cavity modes playing the role of the environment, we study the dynamics of the spontaneous emission. We observe a change from non-Markovian to Markovian decay in the presence of disorder by tuning the correlation parameter. This is associated with a localization-delocalization transition involving the field modes. Two dissipative models that effectively reproduce the behavior of the non-Markovianity are discussed. The dissipation dynamics of the atom can thus be used to extract information about the phase of the environment. Our results provide a direction in the engineering of disordered quantum systems to function as controllable reservoirs.

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arXiv2024

Non-Markovianity in High-Dimensional Open Quantum Systems using Next-generation Multicore Optical Fibers

With the advent of quantum technology, the interest in communication tasks assisted by quantum systems has increased both in academia and industry. Nonetheless, the transmission of a quantum state in real-world scenarios is bounded by environmental noise, so that the quantum channel is an open quantum system. In this work, we study a high-dimensional open quantum system in a multicore optical fiber by characterizing the environmental interaction as quantum operations corresponding to probabilistic phase-flips. The experimental platform is currently state-of-the-art for quantum information processing with multicore fibers. At a given evolution stage we observe a non-Markovian behaviour of the system, which is demonstrated through a proof-of-principle implementation of the Quantum Vault protocol. A better understanding of phase-noise in multicore fibers will improve several real-world communication protocols, since they are a prime candidate to be adopted in future telecom networks.

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arXiv2024

Distillation of quantum non-Markovianity

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.

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arXiv2024

Petz recovery maps for qudit quantum channels

This study delves into the efficacy of the Petz recovery map within the context of two paradigmatic quantum channels: dephasing and amplitude-damping. While prior investigations have predominantly focused on qubits, our research extends this inquiry to higher-dimensional systems. We introduce a novel, state-independent framework based on the Choi-Jamiołkowski isomorphism to evaluate the performance of the Petz map. By analyzing different channels and the (non-)unital nature of these processes, we emphasize the pivotal role of the reference state selection in determining the map's effectiveness. Furthermore, our analysis underscores the considerable impact of suboptimal choices on performance, prompting a broader consideration of factors such as system dimensionality.

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arXiv2023

Statistical properties and repetition rates for a quantum network with geographical distribution of nodes

Steady technological advances and recent milestones such as intercontinental quantum communication and the first implementation of medium-scale quantum networks are paving the way for the establishment of the quantum internet, a network of nodes interconnected by quantum channels. Here we build upon recent models for quantum networks based on optical fibers by considering the effect of a non-uniform distribution of nodes, more specifically based on the demographic data of the federal states in Brazil. We not only compute the statistical properties of this more realistic network, comparing its features with previous models but also employ it to compute the repetition rates for entanglement swapping, an essential protocol for quantum communication based on quantum repeaters.

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arXiv2022

Harmonic oscillator kicked by spin measurements: a Floquet-like system without classical analogous

We present a kicked harmonic oscillator where the impulsive driving is provided by stroboscopic measurements on an ancillary degree of freedom and not by the canonical quantization of a time-dependent Hamiltonian. The ancila is dynamically entangled with the oscillator position, while the background Hamiltonian remains static. The dynamics of this system is determined in closed analytical form, allowing for the evaluation of a properly defined Loschmidt echo, ensemble averages, and phase-space portraits. As in the case of standard Floquet systems we observe regimes with crystalline and quasicrystalline structures in phase space, resonances, and evidences of chaotic behavior, however, not originating from any classically chaotic system.

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arXiv2022

Approximating Invertible Maps by Recovery Channels: Optimality and an Application to Non-Markovian Dynamics

We investigate the problem of reversing quantum dynamics, specifically via optimal Petz recovery maps. We focus on typical decoherence channels, such as dephasing, depolarizing and amplitude damping. We illustrate how well a physically implementable recovery map simulates an inverse evolution. We extend this idea to explore the use of recovery maps as an approximation of inverse maps, and apply it in the context of non-Markovian dynamics. We show how this strategy attenuates non-Markovian effects, such as the backflow of information.

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arXiv2019

A correlation measure detecting almost all non-Markovian evolutions

We investigate the ability of correlation measures to witness non-Markovian open quantum system dynamics. It is shown that the mutual information and any entanglement measure between the system and an ancilla do not witness all non-Markovian dynamics. A correlation measure is introduced, and it is proven that, in an enlarged setting with two ancillary systems, this measure detects almost all non-Markovian dynamics, except possibly a zero-measure set of dynamics that is non-bijective in finite time-intervals. Our proof is constructive and provides different initial states detecting the non-Markovian evolutions. These states are all separable and some are arbitrarily close to a product state.

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arXiv2019

Witnessing non-Markovian dynamics through correlations

Non-Markovian effects in an open-system dynamics are usually associated to information backflows from the environment to the system. However, the way these backflows manifest and how to detect them is unclear. A natural approach is to study the backflow in terms of the correlations the evolving system displays with another unperturbed system during the dynamics. In this work, we study the power of this approach to witness non-Markovian dynamics using different correlation measures. We identify simple dynamics where the failure of completely-positive divisibility is in one-to-one correspondence with a correlation backflow. We then focus on specific correlation measures, such as those based on entanglement and the mutual information, and identify their strengths and limitations. We conclude with a study of a recently introduced correlation measures based on state distinguishability and see how, for these measures, adding an extra auxiliary system enlarges the set of detectable non-Markovian dynamics.

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arXiv2018

Continuous Monitoring of Energy in Quantum Open Systems

We propose a method to continually monitor the energy of a quantum system. We show that by having some previous knowledge of the system's dynamics, but not all of it, one can use the measured energy to determine many other quantities, such as the work performed on the system, the heat exchanged between the system and a thermal reservoir, the time dependence of the Hamiltonian of the system as well as the total entropy produced by its dynamics. We have also analyzed how this method is dependent on the quality factor of the measurements employed.

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arXiv2017

Emerging dynamics arising from coarse-grained quantum systems

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.

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