Objectivity in a Noisy Photonic Environment through Quantum State Information Broadcasting

Abstract

Recently, the emergence of classical objectivity as a property of a quantum state has been explicitly derived for a small object embedded in a photonic environment in terms of a spectrum broadcast form-a specific classically correlated state, redundantly encoding information about the preferred states of the object in the environment. However, the environment was in a pure state and the fundamental problem was how generic and robust is the conclusion. Here we prove that despite of the initial environmental noise the emergence of the broadcast structure still holds, leading to the perceived objectivity of the state of the object. We also show how this leads to a quantum Darwinism-type condition, reflecting classicality of proliferated information in terms of a limit behavior of the mutual information. Quite surprisingly, we find "singular points" of the decoherence, which can be used to faithfully broadcast a specific classical message through the noisy environment.Keywords: decoherence, quantum darwinism, state broadcasting Uninterrupted series of successes of quantum mechanics supports a belief that quantum formalism applies to all of physical reality. Thus, in particular, the objective classical world of everyday experience should emerge naturally from the formalism. This has been a long-standing problem, already present from the very dawn of quantum mechanics [1, 2]. Recently, a crucial step was made in a series of works (see e.g. [3][4][5]) introducing quantum Darwinism-a refined model of decoherence [6], based on a multiple environments paradigm: A quantum system of interest S interacts with multiple environments E 1 , . . . , E N instead of just one. The authors assumed [3] that each of these independent fractions effectively measures the system and argued that after the decoherence (with some timescale τ D ) it carries nearly complete classical information about the system, meaning that the information propagates in the environment with a huge redundancy. A further step was made in [7] by dropping any explicit assumptions on the dynamics and applying a operational definition of objectivity [4] directly to the post-decoherence quantum state. This, together with the Bohr's criterion of non-disturbance [8], allowed to derive a universal state structure-spectrum broadcast form (cf.[9]), responsible for the appearance of classical objectivity in a model-and dynamics-independent way [7]:There appears an objectively existing state of the system S if the time-asymptotic joint quantum state of S and the observed fraction of the environment f E is of a spectrum broadcast form:(1) with {| x i } a pointer basis [10], p i 's initial pointer probabilities, andsome states of the environments E 1 , . . . , E f N with mutually orthogonal supports.The states (1) "work" by faithfully encoding the same classical information about the system (index i) in each portion of the environment-they describe redundant proliferation (broadcasting) of information, necessary for objectivity [4, 7]. A process of formation of a state (1...

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