In this dissertation we are interested in the dynamics of open quantum systems in the context of quantum information. First, we investigate the dynamics of one qubit at the regime where an inverse evolution is not well defined. This limit is widely used and explored in this work, called as the limit of non-bijectivity. We demonstrate how to compute a completely positive inverse evolution, based on the theory of recovery maps, here to be the Petz recovery map. The analyzed evolutions are the typical decoherence processes: dephasing, depolarizing and amplitude damping channels in the regime of non-bijectivity. To measure how efficient the Petz can be recovering a random quantum state, we use the fidelity function as the figure of merit. Also, we quantify how non-invertible a dynamics is compared to another. As an application for this formalism, in the second part of this work we show how we can explore recovery maps in the context of non-Markovian evolutions, in order to minimize memory effects. We demonstrate that recovering maps can be useful under certain constraints to simulate a non-Markovian evolution by an “almost” Markovian one. We demonstrate that there exists a strong dependence between the success of this strategy and the initial correlations between system and environment.
In this dissertation we are interested in the dynamics of open quantum systems in the context of quantum information. First, we investigate the dynamics of one qubit at the regime where an inverse evolution is not well defined. This limit is widely used and explored in this work, called as the limit of non-bijectivity. We demonstrate how to compute a completely positive inverse evolution, based on the theory of recovery maps, here to be the Petz recovery map. The analyzed evolutions are the typical decoherence processes: dephasing, depolarizing and amplitude damping channels in the regime of non-bijectivity. To measure how efficient the Petz can be recovering a random quantum state, we use the fidelity function as the figure of merit. Also, we quantify how non-invertible a dynamics is compared to another. As an application for this formalism, in the second part of this work we show how we can explore recovery maps in the context of non-Markovian evolutions, in order to minimize memory effects. We demonstrate that recovering maps can be useful under certain constraints to simulate a non-Markovian evolution by an “almost” Markovian one. We demonstrate that there exists a strong dependence between the success of this strategy and the initial correlations between system and environment.
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.
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.
Quantum memory effects can be qualitatively understood as a consequence of an environment-to-system backflow of information. Here, we analyze and compare how this concept is interpreted and implemented in different approaches to quantum non-Markovianity. We study a nonoperational approach, defined by the distinguishability between two system states characterized by different initial conditions, and an operational approach, which is defined by the correlation between different outcomes associated to successive measurement processes performed over the system of interest. The differences, limitations, and vantages of each approach are characterized in detail by considering diverse system-environment models and dynamics. As a specific example, we study a non-Markovian depolarizing map induced by the interaction of the system of interest with an environment characterized by incoherent and coherent self-dynamics.
In this thesis, we discuss aspects of the simulation, characterisation, and control of the dynamics of open quantum systems. The latter are systems governed by quantum mechanical laws and interacting with an environment, which is typically much larger than the system itself. According to the standard approach, one is usually able to perform a suitable average over the environmental degrees of freedom, resulting in an effective description of the main system dynamics, which accounts for the effects of the interaction with the surroundings. In standard scenarios, usually studied within the so-called Born-Markov approximation, the system-environment coupling is weak and such that we can perform a neat separation of timescales: the environmental dynamics is assumed to be fast compared to the typical evolution timescale of the system of interest. However, nowadays we are able to inspect physical scenarios where the usual Born-Markov approximation breaks down: the interaction between system and environment can be strong, likely leading to non-negligible memory (non-Markovian) effects. In this work, we discuss some instances in which we cannot work in the standard Born-Markov regime. We introduce and analyse some numerical and analytical techniques to characterise and simulate non-standard scenarios. We show that, even in the Markovian regime, the traditional formulation of thermodynamic irreversibility shows flaws and inconsistencies. We thus use phase-space methods to assess the role of initial correlations shared by the two parties of a bipartite harmonic system in the entropy production rate, including non-Markovian effects. Furthermore, we show that certain interactions enable to redraw the boundaries between the system and the environment in an effective manner, resulting in a new picture where the system degrees of freedom are augmented, while the residual environment is rearranged in such a way that the Born-Markov approximation is recovered. This analytical technique, known as reaction coordinate mapping approach, is employed in this work to show that, upon an accurate choice of the parameter regime, a spin-boson model can serve as a quantum analogue simulator of non-Markovian multiphoton Jaynes-Cummings models. These systematic studies shed light on the thermodynamic characterisation of open quantum systems, as well as on their numerical simulation.
The quantum information lost in open evolutions cannot be fully recovered, but partial recovery is possible. The Petz recovery map guarantees almost optimal recovery, notably if the chosen reference state is close to the real one. This map has been widely used in theoretical studies, but has been the object of only a handful of experimental realisations, typically under a single fixed noise model. In this work, we describe and implement the Petz recovery map for a versatile class of qubit channels with tunable decoherence and dissipation. The setup we realize is also the first experimental example of ``tabletop reversibility'': for a good range of choices of the reference state, the Petz recovery map can be implemented with the same devices as the forward dissipative evolution, whose effect it is partially undoing. Our results demonstrate that the Petz recovery map can be resource-efficiently realized without requiring complex ancillary resources, providing a feasible pathway for mitigating information loss in quantum systems.
We consider the problem of quantum error correction (QEC) for non-Markovian noise. Using the well-known Petz recovery map, we first show that conditions for approximate QEC can be easily generalized for the case of non-Markovian noise in the strong-coupling regime where the noise map becomes non-completely-positive at intermediate times. While certain approximate QEC schemes are ineffective against quantum non-Markovian noise, in the sense that the fidelity vanishes in finite time, the Petz map adapted to non-Markovian noise uniquely safeguards the code space even at the maximum noise limit. Focusing on the case of non-Markovian amplitude damping noise, we further show that the non-Markovian Petz map also outperforms the standard, stabilizer-based QEC code. Since implementing such a non-Markovian map poses practical challenges, we also construct a Markovian Petz map that achieves a similar performance, with only a slight compromise on the fidelity. Finally, we also study an example of non-Markovian Pauli noise, namely the non-Markovian dephasing channel. In this case, we show that the non-Markovian Petz recovery preserves the code space even at the high-noise limit for certain noise-adapted codes, whereas the Markovian Petz and stabilizer recoveries are ineffective.