Objectivity constitutes one of the main features of the macroscopic classical world. An important aspect of the quantum-to-classical transition issue is to explain how such a property arises from the microscopic quantum theory. Recently, within the framework of open quantum systems, there has been proposed such a mechanism in terms of the so-called spectrum broadcast structures. These are multipartite quantum states of the system of interest and a part of its environment, assumed to be under an observation. This approach requires a departure from the standard open quantum systems methods, as the environment cannot be completely neglected. In the present paper we study the emergence of such a state structure in one of the canonical models of the condensed-matter theory: the spin-boson model, describing the dynamics of a two-level system coupled to an environment made up by a large number of harmonic oscillators. We pay much attention to the behavior of the model in the non-Markovian regime, in order to provide a testbed to analyze how the non-Markovian nature of the evolution affects the surfacing of a spectrum broadcast structure.
Objectivity constitutes one of the main features of the macroscopic classical world. An important aspect of the quantum-to-classical transition issue is to explain how such a property arises from the microscopic quantum theory. Recently, within the framework of open quantum systems, there has been proposed such a mechanism in terms of the so-called spectrum broadcast structures. These are multipartite quantum states of the system of interest and a part of its environment, assumed to be under an observation. This approach requires a departure from the standard open quantum systems methods, as the environment cannot be completely neglected. In the present paper we study the emergence of such a state structure in one of the canonical models of the condensed-matter theory: the spin-boson model, describing the dynamics of a two-level system coupled to an environment made up by a large number of harmonic oscillators. We pay much attention to the behavior of the model in the non-Markovian regime, in order to provide a testbed to analyze how the non-Markovian nature of the evolution affects the surfacing of a spectrum broadcast structure.
Classical objectivity as a property of quantum states —a view proposed to explain the observer-independent character of our world from quantum theory, is an important step in bridging the quantum-classical gap. It was recently derived in terms of spectrum broadcast structures for small objects embedded in noisy photon-like environments. However, two fundamental problems have arisen: a description of objective motion and applicability to other types of environments. Here we derive an example of objective states of motion in quantum mechanics by showing the formation of dynamical spectrum broadcast structures in the celebrated, realistic model of decoherence —Quantum Brownian Motion. We do it for realistic, thermal environments and show their noise-robustness. This opens a potentially new method of studying the quantum-to-classical transition.
Quantum mechanics describes the smallest systems, whilst classical physics describes macroscopic scales. However, the quantum-to-classical transition is a major unsolved problem. In this thesis, we develop further understanding of the transition through the concept of objectivity. The objects we perceive in our everyday world are objective: they exist regardless of observation, and their properties are independent of observers. This is because information about everyday objects came be found, for example, in the surrounding photon environment. Quantum Darwinism is a conceptual and theoretical framework that describes the emergence of objectivity. The “Darwinistic” part refers to how certain types of information tends to spread at the expense of others. The thesis addresses the quantitative description of objectivity, the dynamics of emergent objectivity, and the analysis of non-objectivity in experimental and biology-inspired systems. Firstly, we propose two new mathematical frameworks to describe objectivity, Strong Quantum Darwinism and invariant spectrum broadcast structure. Then we unite them with the pre-existing frameworks, Zurek's Quantum Darwinism and spectrum broadcast structure, by identifying their deep connections and differences. These conditions highlight how Each framework considers varying amounts of objectivity in the system and environments and together, they create a hierarchy of objectivity. We then analyse objectivity in a scenario where system-environment interactions are strong and non-Markovian, highlighting some practical differences between the Quantum Darwinism frameworks. Next, we describe the quantum channels that create objective states, leading us to discuss the contribution of non-Markovianity to the emergence of objectivity. Then, we introduce a witnessing scheme that simplifies the detection of non-objectivity to promote further experimental testing of Quantum Darwinism with larger environments. Finally, we examine the contribution of quantum coherence and non-objectivity to the performance of a biological-inspired quantum magnetic sensor that operates close to the quantum-classical boundary. We find that the sensor operates in a non-objective regime, and that quantum coherence is necessary for the sensor's performance. The quantum-to-classical transition is a longstanding open question: these findings deepen our knowledge of how objectivity emerges, and contributes to and the types of interactions that keep systems quantum, which is relevant for understanding quantum biological systems and exploiting environment effects in novel quantum technologies. While the quantum-to-classical transition remains unsolved, Quantum Darwinism and its frameworks contribute to the understanding of emergent objectivity and have much potential to further explore aspects of the transition within the structure of quantum mechanics.
We investigate quantum objectivity in the boson-spin model, where a central harmonic oscillator interacts with a thermal bath of spin-21 systems. We analyze how information about a continuous position variable can be encoded into discrete, finite-dimensional environments. More precisely, we study conditions under which the so-called spectrum broadcast structures can be formed in the model. These are multipartite quantum-state structures, representing a mode-refined form of decoherence. Working in the recoil-less limit, we use the Floquet theory to show that despite its apparent simplicity, the model has a rich structure with different regimes, depending on the motion of the central system. In one of them, the faithful encoding of the position and hence objectivity are impossible irrespectively of the resources used. In another, large enough collections of spins will faithfully encode the position information. We derive the characteristic length scales, corresponding to decoherence and precision of the encoding.
Digital quantum computers have the potential to simulate complex quantum systems. The spin-boson model is one of such systems, used in disparate physical domains. Importantly, in a number of setups, the spin-boson model is open, i.e., the system is in contact with an external environment which can, for instance, cause the decay of the spin state. Here, we study how to simulate such open quantum dynamics in a digital quantum computer, for which we use an IBM hardware. We consider in particular how accurate different implementations of the evolution result as a function of the level of noise in the hardware and of the parameters of the open dynamics. For the regimes studied, we show that the key aspect is to simulate the unitary portion of the dynamics, while the dissipative part can lead to a more noise-resistant simulation. We consider both a single spin coupled to a harmonic oscillator, and also two spins coupled to the oscillator. In the latter case, we show that it is possible to simulate the emergence of correlations between the spins via the oscillator.
Quantum Darwinism and spectrum broadcast structure describe the emergence of objectivity in quantum systems. However, it is unclear whether these two frameworks lead to consistent predictions on the objectivity of the state of a quantum system in a given scenario. In this paper, we jointly investigate quantum Darwinism and spectrum broadcasting, as well as the subdivision of quantum Darwinism into accessible information and quantum discord, in a two-level system interacting with an N-level environment via a random matrix coupling. We propose a novel partial trace method to suitably and consistently partition the effective N-level environment, and compare the predictions with those obtained using the partitioning method proposed by Perez [Phys. Rev. A 81, 052326 (2010)]. We find that Quantum Darwinism can apparently emerge even when spectrum broadcast structure does not emerge, and the majority of the quantum mutual information between system and environment fractions is in fact quantum in nature. This work therefore shows there can be discrepancies between quantum Darwinism, and the nature of information and spectrum broadcast structure.
The birth of objective properties from the subjective quantum world has been one of the key questions in the quantum-to-classical transition. Based on recent results in the field, we study it in a quantum mechanical model of a boson-boson interaction—quantum Brownian motion. Using various simplifications, we prove a formation for thermal environments of, so called, spectrum broadcast structures, responsible for perceived objectivity. In the quantum measurement limit we prove that this structure is always formed, providing the characteristic timescales. Including self-Hamiltonians of the environment, we show the exponential scaling of the effect with the size of the environment. Finally, in the full model we numerically study the influence of squeezing in the initial state of the environment, showing broader regions of formation than for non-squeezed thermal states.