Redundant information in a spin system beyond pure decoherence

We lay a comprehensive foundation for the study of redundant information storage in decoherence processes. Redundancy has been proposed as a prerequisite for objectivity, the defining property of classical objects. We consider two ensembles of states for a model universe consisting of one system and many environments: the first consisting of arbitrary states, and the second consisting of ``singly branching'' states consistent with a simple decoherence model. Typical states from the random ensemble do not store information about the system redundantly, but information stored in branching states has a redundancy proportional to the environment's size. We compute the specific redundancy for a wide range of model universes, and fit the results to a simple first-principles theory. Our results show that the presence of redundancy divides information about the system into three parts: classical (redundant); purely quantum; and the borderline, undifferentiated or ``nonredundant,'' information.We lay a comprehensive foundation for the study of redundant information storage in decoherence processes. Redundancy has been proposed as a prerequisite for objectivity, the defining property of classical objects. We consider two ensembles of states for a model universe consisting of one system and many environments: the first consisting of arbitrary states, and the second consisting of ``singly branching'' states consistent with a simple decoherence model. Typical states from the random ensemble do not store information about the system redundantly, but information stored in branching states has a redundancy proportional to the environment's size. We compute the specific redundancy for a wide range of model universes, and fit the results to a simple first-principles theory. Our results show that the presence of redundancy divides information about the system into three parts: classical (redundant); purely quantum; and the borderline, undifferentiated or ``nonredundant,'' information.

arXiv:quant-ph/0505031Physical Review AJun 8, 2006207 citations

Quantum Darwinism and objectivity in non-trivial systems and interactions

Eoghan Ryan

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.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.

Oct 1, 20260 citations

Decoherence in Quantum Spin Systems

V. V. Dobrovitski

Bulletin of the American Physical SocietyMar 13, 20060 citations

Decoherence on Quantum Spin Systems

Philip C. E. Stamp

Bulletin of the American Physical SocietyMar 24, 20050 citations

Redundant imprinting of information in nonideal environments: Objective reality via a noisy channel

Michael P. Zwolak, H. T. Quan, Wojciech Hubert Zurek

Quantum Darwinism provides an information-theoretic framework for the emergence of the objective, classical world from the quantum substrate. The key to this emergence is the proliferation of redundant information throughout the environment where observers can then intercept it. We study this process for a purely decohering interaction when the environment, $\mathcal{E}$ , is in a nonideal (e.g., mixed) initial state. In the case of good decoherence, that is, after the pointer states have been unambiguously selected, the mutual information between the system, $\mathcal{S}$ , and an environment fragment, $\mathcal{F}$ , is given solely by $\mathcal{F}$ 's entropy increase. This demonstrates that the environment's capacity for recording the state of $\mathcal{S}$ is directly related to its ability to increase its entropy. Environments that remain nearly invariant under the interaction with $\mathcal{S}$ , either because they have a large initial entropy or a misaligned initial state, therefore have a diminished ability to acquire information. To elucidate the concept of good decoherence, we show that, when decoherence is not complete, the deviation of the mutual information from $\mathcal{F}$ 's entropy change is quantified by the quantum discord, i.e., the excess mutual information between $\mathcal{S}$ and $\mathcal{F}$ is information regarding the initial coherence between pointer states of $\mathcal{S}$ . In addition to illustrating these results with a single-qubit system interacting with a multiqubit environment, we find scaling relations for the redundancy of information acquired by the environment that display a universal behavior independent of the initial state of $\mathcal{S}$ . Our results demonstrate that Quantum Darwinism is robust with respect to nonideal initial states of the environment: the environment almost always acquires redundant information about the system but its rate of acquisition can be reduced.Quantum Darwinism provides an information-theoretic framework for the emergence of the objective, classical world from the quantum substrate. The key to this emergence is the proliferation of redundant information throughout the environment where observers can then intercept it. We study this process for a purely decohering interaction when the environment, $\mathcal{E}$, is in a nonideal (e.g., mixed) initial state. In the case of good decoherence, that is, after the pointer states have been unambiguously selected, the mutual information between the system, $\mathcal{S}$, and an environment fragment, $\mathcal{F}$, is given solely by $\mathcal{F}$'s entropy increase. This demonstrates that the environment's capacity for recording the state of $\mathcal{S}$ is directly related to its ability to increase its entropy. Environments that remain nearly invariant under the interaction with $\mathcal{S}$, either because they have a large initial entropy or a misaligned initial state, therefore have a diminished ability to acquire information. To elucidate the concept of good decoherence, we show that, when decoherence is not complete, the deviation of the mutual information from $\mathcal{F}$'s entropy change is quantified by the quantum discord, i.e., the excess mutual information between $\mathcal{S}$ and $\mathcal{F}$ is information regarding the initial coherence between pointer states of $\mathcal{S}$. In addition to illustrating these results with a single-qubit system interacting with a multiqubit environment, we find scaling relations for the redundancy of information acquired by the environment that display a universal behavior independent of the initial state of $\mathcal{S}$. Our results demonstrate that Quantum Darwinism is robust with respect to nonideal initial states of the environment: the environment almost always acquires redundant information about the system but its rate of acquisition can be reduced.

arXiv:0911.4307Physical Review AJun 10, 201071 citations

\mathcal{E}

, is in a nonideal (e.g., mixed) initial state. In the case of good decoherence, that is, after the pointer states have been unambiguously selected, the mutual information between the system,

\mathcal{S}

, and an environment fragment,

\mathcal{F}

, is given solely by

\mathcal{F}

's entropy increase. This demonstrates that the environment's capacity for recording the state of

\mathcal{S}

is directly related to its ability to increase its entropy. Environments that remain nearly invariant under the interaction with

\mathcal{S}

, either because they have a large initial entropy or a misaligned initial state, therefore have a diminished ability to acquire information. To elucidate the concept of good decoherence, we show that, when decoherence is not complete, the deviation of the mutual information from

\mathcal{F}

's entropy change is quantified by the quantum discord, i.e., the excess mutual information between

\mathcal{S}

and

\mathcal{F}

is information regarding the initial coherence between pointer states of

\mathcal{S}

. In addition to illustrating these results with a single-qubit system interacting with a multiqubit environment, we find scaling relations for the redundancy of information acquired by the environment that display a universal behavior independent of the initial state of

\mathcal{S}

. Our results demonstrate that Quantum Darwinism is robust with respect to nonideal initial states of the environment: the environment almost always acquires redundant information about the system but its rate of acquisition can be reduced.