We investigate the implications of quantum Darwinism in a composite quantum system with interacting constituents exhibiting a decoherence-free subspace. We consider a two-qubit system coupled to an N-qubit environment via a dephasing interaction. For excitation preserving interactions between the system qubits, an analytical expression for the dynamics is obtained. It demonstrates that part of the system Hilbert space redundantly proliferates its information to the environment, while the remaining subspace is decoupled and preserves clear non-classical signatures. For measurements performed on the system, we establish that a non-zero quantum discord is shared between the composite system and the environment, thus violating the conditions of strong Darwinism. However, due to the asymmetry of quantum discord, the information shared with the environment is completely classical for measurements performed on the environment. Our results imply a dichotomy between objectivity and classicality that emerges when considering composite systems.
We investigate the implications of quantum Darwinism in a composite quantum system with interacting constituents exhibiting a decoherence-free subspace. We consider a two-qubit system coupled to an N-qubit environment via a dephasing interaction. For excitation preserving interactions between the system qubits, an analytical expression for the dynamics is obtained. It demonstrates that part of the system Hilbert space redundantly proliferates its information to the environment, while the remaining subspace is decoupled and preserves clear non-classical signatures. For measurements performed on the system, we establish that a non-zero quantum discord is shared between the composite system and the environment, thus violating the conditions of strong Darwinism. However, due to the asymmetry of quantum discord, the information shared with the environment is completely classical for measurements performed on the environment. Our results imply a dichotomy between objectivity and classicality that emerges when considering composite systems.
The framework of Quantum Darwinism strives at characterizing the quantum-to-classical transition by introducing the concept of redundancy of information-as measured by Mutual Information-that a set of observers would acquire on the state of a physical system of interest. Further development on this concept, in the form of Strong Quantum Darwinism and Spectrum Broadcast Structures, has recently led to a more fine-grained identification of the nature of such information, which should not involve any quantum correlations between observing and observed systems, while the assessment of information proliferation from individual systems has attracted most of the attention so far, the way such mechanism takes place in more complex states is open to exploration. To this end, we shall consider a two-qubit state, sharing initial quantum correlations in the form of Quantum Discord, and different dephasing-like interactions between them and an observing environment. We will focus on the amount of information regarding the subsystem not involved in the interaction that is proliferated to the environment. We shall refer to this as mediated redundancy. We will show that, in some cases, the channel capacity of the subsystems, given these interactions, can exceed that of the fragments.
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 explains classical objectivity through redundant environmental records of a system's pointer states. We show that these records can be established through an intermediate measurement apparatus without direct system--environment interactions. Using exact analytical solutions of quantum circuit models, we compare system monitoring with apparatus monitoring, where the environment interacts only with the apparatus. During encoding, system--apparatus correlations decrease as system--environment correlations grow. Without noise, both models yield identical accessible pointer information and redundancy, while the discord accounts for their different mutual information. The reliability of these records depends on where noise acts. Apparatus bit flips introduce errors shared by successive records, limiting the information recoverable even from the complete environment. In contrast, larger fragments can mitigate independent noise on environment qubits after encoding. Dephasing in the pointer basis leaves the record information unchanged in the model considered. These results extend the description of quantum Darwinism to indirect measurements and clarify the conditions for reliable environmental records.
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 Darwinism extends the traditional formalism of decoherence to explain the emergence of classicality in a quantum universe. A classical description emerges when the environment tends to redundantly acquire information about the pointer states of an open system. In light of recent interest, we apply the theoretical tools of the framework to a qubit coupled with many bosonic subenvironments. We examine the degree to which the same classical information is encoded across collections of (i) complete subenvironments and (ii) residual ``pseudomode'' components of each subenvironment, the conception of which provides a dynamic representation of the reservoir memory. Overall, significant redundancy of information is found as a typical result of the decoherence process. However, by examining its decomposition in terms of classical and quantum correlations, we discover classical information to be nonredundant in both cases i and ii. Moreover, with the full collection of pseudomodes, certain dynamical regimes realize opposite effects, where either the total classical or quantum correlations predominantly decay over time. Finally, when the dynamics are non-Markovian, we find that redundant information is suppressed in line with information backflow to the qubit. By quantifying redundancy, we concretely show it to act as a witness to non-Markovianity in the same way as the trace distance does for nondivisible dynamical maps.
Quantum Darwinism attempts to explain the emergence of objective reality of the state of a quantum system in terms of redundant information about the system acquired by independent noninteracting fragments of the environment. The consideration of interacting environmental elements gives rise to a rich phenomenology, including the occurrence of non-Markovian features, whose effects on objectification in the manner of quantum Darwinism needs to be fully understood. We study a model of local interaction between a simple quantum system and a multimode environment that allows for a clear investigation of the interplay between information trapping and propagation in the environment and the emergence of quantum Darwinism. We provide strong evidence of the correlation between non-Markovianity and quantum Darwinism in such a model, thus providing strong evidence of a potential link between such fundamental phenomena.