Quantum Darwinism: Entanglement, branches, and the emergent classicality of redundantly stored quantum information

Abstract

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 ͑redundant͒; purely quantum; and the borderline, undifferentiated or "nonredundant," information.

Physics: Quantum all the way

“…These robust states are those that feature in classical physics, such as position and its rate of change, which is associated with momentum. In a sense, these are the 'fittest' states -which is why Zurek and his colleagues call their idea quantum darwinism 4,5 .…”

Quantum Darwinism and non-Markovian dissipative dynamics from quantum phases of the spin-1/2XXmodel

“…This characteristic behavior is illustrated in Refs. [19,20]. In turn, states created by decoherence, which do not follow this behavior and are those explaining our everyday classical experience, have zero measure in the thermodynamic limit.…”

Observables can be tailored to change the entanglement of any pure state

“…Such observableinduced partitions of the Hilbert space have been referred to as virtual subsystems and can be thought of as a generalization from entanglement between subsystems to entanglement between degrees of freedom (see also [3,4]). This mathematical framework has found applications to studies of multi-level encoding [5], decoherence [6], operator quantum error correction [7], entanglement in fermionic systems [8], single-particle entanglement [9,10], and entanglement in scattering systems [11].In this Letter, we extend this mathematical framework and prove what we call the Tailored Observables Theorem (Theorem 6): observables can be constructed such that any pure state in a finite-dimensional Hilbert space H = C d has any amount of entanglement possible for any given factorization of the dimension d of H. This means all pure states are equivalent as entanglement resources in the ideal case of complete control of observables. To establish the framework, we provide a brief, relatively self-contained introduction to Zanardi's Theorem and obtain some necessary preliminary results about observable algebras in finite dimensions.…”

“…Such observableinduced partitions of the Hilbert space have been referred to as virtual subsystems and can be thought of as a generalization from entanglement between subsystems to entanglement between degrees of freedom (see also [3,4]). This mathematical framework has found applications to studies of multi-level encoding [5], decoherence [6], operator quantum error correction [7], entanglement in fermionic systems [8], single-particle entanglement [9,10], and entanglement in scattering systems [11].…”