Quantum systems achieve objectivity by redundantly encoding information about themselves into the surrounding environment, through a mechanism known as quantum Darwinism. When this happens, observers measure the environment and infer the system to be in one of its pointer states. We study the emergence of objectivity whenever the Hamiltonian of the system and the interaction Hamiltonian between system and environment do not commute, a condition where it becomes difficult to identify pointer states, and the use of methods such as the predictability sieve becomes necessary. We show in an explicit qubit model to what degree the noncommuting evolution allows for the emergence of objective states, and show that a definition of pointer states based on spectrum broadcast structure is more natural in this context, and coincides with the one based on the predictability sieve for commuting evolutions.
Quantum systems achieve objectivity by redundantly encoding information about themselves into the surrounding environment, through a mechanism known as quantum Darwinism. When this happens, observers measure the environment and infer the system to be in one of its pointer states. We study the emergence of objectivity whenever the Hamiltonian of the system and the interaction Hamiltonian between system and environment do not commute, a condition where it becomes difficult to identify pointer states, and the use of methods such as the predictability sieve becomes necessary. We show in an explicit qubit model to what degree the noncommuting evolution allows for the emergence of objective states, and show that a definition of pointer states based on spectrum broadcast structure is more natural in this context, and coincides with the one based on the predictability sieve for commuting evolutions.
An explanation for the quantum-to-classical transition has long been sought after since the haydays of the field. Decoherence theory and open quantum system dynamics have paved the way, showing how a system can become correlated with, and so lose information into the environment. Quantum Darwinism, and its more stringent cousins Strong Quantum Darwinism and Spectrum Broadcast Structures, seek to explain how this information loss is achieved in such a way as to be objective, classical and redundant. However there remains questions as to how the structure of the environment, states and types of interactions can give rise to this redundant encoding. In this thesis, we collect the work of 3 of our papers, exploring these questions. First, we show how information from one environment can spread to another. Then we show how commutativity can play a role in the emergence of objectivity. Lastly, we move beyond a single, pure system to a more realistic bipartite one, with both classical and quantum correlations between the subsystems. We shall show how interactions between only these subsystems can mediate the redundancy of others, and how these can lower bound and upper bound other forms of interactions between said subsystems and the environment.
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 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 under the Perez trace 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.
This paper examines the role of Quantum Darwinism in explaining the emergence of classical objectivity within The Many-Worlds Interpretation of quantum mechanics. Decoherence explains why macroscopically distinct alternatives become practically inaccessible to local observers, but it does not by itself explain why multiple observers can independently agree on the same classical state. Quantum Darwinism strengthens this account by describing how information about stable pointer states becomes redundantly encoded in environmental fragments. However, this paper argues that redundancy is necessary for objectivity but not enough to explain objectivity. A simple qubit test model implemented in Qiskit is used to demonstrate redundant environmental coding. The discussion connects this claim to Strong Quantum Darwinism, Spectrum Broadcast Structure, and Quantum Discord, which sharpen the distinction between mere correlation and objective classical records. Finally, this paper proposes phase anti-redundancy as a future direction; While pointer state information becomes locally redundant, cross-branch phase information appears to remain globally encoded and increasingly difficult to recover. This suggests that branch objectivity may require not only redundant classical records, but also the fact that cross-branch phase information is encoded in global correlations rather than in locally accessible environmental fragments.
Quantum Darwinism demonstrates not only that preferred states are selected for their stability but also that information about them is broadcast by the same environment that causes decoherence and einselection. That environment acts both as a censor and as an advertising agent that disseminates information about pointer states while suppressing complementary information. Chapter 8 explores the implications and limitations of quantum Darwinism using models inspired by the structure of the Universe we inhabit. We perceive our Universe using light and other means of information transmission. We explore models that have a well-defined relation with our everyday reality, and where one can also selectively relax some of the idealized assumptions and investigate the consequences. Light is the communication channel through which we obtain most of our information. Fortunately, it is an ideal channel in the sense of quantum Darwinism, and simple but realistic cases are exactly solvable. The solution presented herein demonstrates the inevitability of the consensus between observers who rely on scattered photons: The emergence of classical objective reality (classical because pointer states are einselected, and objective because redundancy imposes consensus) is inevitable. This is how the classical world we perceive emerges from within the quantum Universe we inhabit.
Quantum Darwinism explains the emergence of classical objectivity within a quantum universe. However, to date, most research on quantum Darwinism has focused on specific models and their stationary properties. To further our understanding of the quantum-to-classical transition, it appears desirable to identify the general criteria a Hamiltonian has to fulfill to support classical reality. To this end, we categorize all N-qubit models with two-body interactions, and show that only those with separable interaction of the system and environment can support a pointer basis. We further demonstrate that “perfect” quantum Darwinism can only emerge if there are no intra-environmental interactions. Our analysis is complemented by solving the ensuing dynamics. We find that in systems exhibiting information scrambling, the dynamical emergence of classical objectivity directly competes with the non-local spread of quantum correlations. Our rigorous findings are illustrated through the numerical analysis of four representative models.
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.