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 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 …
A simple toy model is proposed that would allow conscious perceptions to be either classical (perceptions of objects without large quantum uncertainties or variances) or highly quantum (e.g., having large variances in the perceived position within a single perception), and yet for which plausible quantum states exhibiting Quantum Darwinism would lead to much higher measures for the classical perceptions.
According to the so-called ``Quantum Darwinist'' approach, the emergence of ``classical islands'' from a quantum background is assumed to obey a (selection) principle of maximal information. We illustrate this idea by considering the coupling of two particles that interact through a position-dependent potential. This approach sheds a new light on the emergence of classical logics and of our classical preconceptions about the world. The distinction between internal and external world, the Cartesian prejudice according to which the whole can be reduced to the sum of its parts and the appearance …
Multiple observers who interact with environmental encodings of the states of a macroscopic quantum system S as required by quantum Darwinism cannot demonstrate that they are jointly observing S without a joint a priori assumption of a classical boundary separating S from its environment E. Quantum Darwinism cannot, therefore, be regarded as providing a purely quantum-mechanical explanation of the "emergence" of classicality.
Observers restricted to the observation of pointer states of apparatus cannot conclusively demonstrate that the pointer of an apparatus A registers the state of a system of interest S without perturbing S. Observers cannot, therefore, conclusively demonstrate that the states of a system S are redundantly encoded by pointer states of multiple independent apparatus without destroying the redundancy of encoding. The redundancy of encoding required by quantum Darwinism must, therefore, be assumed from outside the quantum-mechanical formalism and without the possibility of experimental demonstratio…
To explain aspects of the quantum-to-classical transition, quantum Darwinism explores the fact that, due to interactions between a quantum open system and its surrounding environment, information about the system can be spread redundantly to the environment. Here we recall that there are in the literature two distinct and non-equivalent ways to make this statement precise and quantitative. We first point out the difference with some simple but illustrative examples. We then consider a model where Darwinism can be seen from both perspectives. Moreover, the non-Markovianity of our model can be v…
Quantum Darwinism posits that the emergence of a classical reality relies on the spreading of classical information from a quantum system to many parts of its environment. But what are the essential physical principles of quantum theory that make this mechanism possible? We address this question by formulating the simplest instance of Darwinism - CNOT-like fan-out interactions - in a class of probabilistic theories that contain classical and quantum theory as special cases. We determine necessary and sufficient conditions for any theory to admit such interactions. We find that every theory wit…
As quantum information science approaches the goal of constructing quantum computers, understanding loss of information through decoherence becomes increasingly important. The information about a system that can be obtained from its environment can facilitate quantum control and error correction. Moreover, observers gain most of their information indirectly, by monitoring (primarily photon) environments of the "objects of interest." Exactly how this information is inscribed in the environment is essential for the emergence of "the classical" from the quantum substrate. In this paper, we examin…
Effective classicality of a property of a quantum system can be defined using redundancy of its record in the environment. This allows quantum physics to approximate the situation encountered in the classical world: The information about a classical system can exist independently from its state. In quantum theory this is no longer possible: In an isolated quantum system the state and the information about it are inextricably linked, and any measurement may -- and usually will -- reset that state. However, when the information about the state of a quantum system is spread throughout the environ…
Quantum Darwinism explains the emergence of classical reality from the underlying quantum reality by the fact that a quantum system is observed indirectly, by looking at parts of its environment, so that only specific information about the system that is redundantly proliferated to many parts of the environment becomes accessible and objective. However it is not clear under what conditions this mechanism holds true. Here we rigorously prove that the emergence of classicality is a general feature of any quantum dynamics: observers who acquire information about a quantum system indirectly have a…
Quantum Darwinism explains the emergence of a classical description of objects in terms of the creation of many redundant registers in an environment containing their classical information. This amplification phenomenon, where only classical information reaches the macroscopic observer and through which different observers can agree on the objective existence of such object, has been revived lately for several types of situations, successfully explaining classicality. We explore quantum Darwinism in the setting of an environment made of two level systems which are initially prepared in the gro…
Quantum Darwinism proposes that the proliferation of redundant information plays a major role in the emergence of objectivity out of the quantum world. Is this kind of objectivity necessarily classical? We show that if one takes Spekkens' notion of noncontextuality as the notion of classicality and the approach of Brandão, Piani and Horodecki to quantum Darwinism, the answer to the above question is `yes', if the environment encodes sufficiently well the proliferated information. Moreover, we propose a threshold on this encoding, above which one can unambiguously say that classical objectivity…
Quantum Darwinism and the quality of Petz recovery
University of Helsinki（赫尔辛基大学）；InstituteQ - the Finnish Quantum Institute（芬兰量子研究所）；Helsinki Institute of Physics（赫尔辛基物理研究所）；QTF Centre of Excellence, Department of Physics, University of Helsinki（赫尔辛基大学物理系量子技术卓越中心）
How the objective everyday world emerges from the underlying quantum behaviour of its microscopic constituents is an open question at the heart of the foundations of quantum mechanics. Quantum Darwinism and spectrum broadcast structure are two different frameworks providing key insight into this question. Recent works, however, indicate these two frameworks can lead to conflicting predictions on the objectivity of the state of a system interacting with an environment. Here we provide a resolution to this issue by defining strong quantum Darwinism and proving that it is equivalent to spectrum b…
Core quantum postulates including the superposition principle and the unitarity of evolutions are natural and strikingly simple. I show that -- when supplemented with a limited version of predictability (captured in the textbook accounts by the repeatability postulate) -- these core postulates can account for all the symptoms of classicality. In particular, both objective classical reality and elusive information about reality arise, via quantum Darwinism, from the quantum substrate.
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 sub-environments. We examine the degree to which the same classical information is encoded across collections of: (i) complete sub-environments, and (ii) residual "pseudomode" components of each sub-environment, the c…
In this article I aim to provide an intuitive and non-technical introduction to decoherence and quantum Darwinism. Together these theories explain how our classical reality emerges from an underlying quantum mechanical description. Here I focus on two aspects of this and explain, firstly, how decoherence can tell us why we never see macroscopic superpositions, such as dead-and-alive cats, in our classical surroundings; and secondly I describe and then provide a resolution to the so-called preferred basis problem. I then introduce recent results demonstrating that certain aspects of classicalit…
We establish bounds on quantum correlations in many-body systems. They reveal what sort of information about a quantum system can be simultaneously recorded in different parts of its environment. Specifically, independent agents who monitor environment fragments can eavesdrop only on amplified and redundantly disseminated - hence, effectively classical - information about the decoherence-resistant pointer observable. We also show that the emergence of classical objectivity is signaled by a distinctive scaling of the conditional mutual information, bypassing hard numerical optimizations. Our re…
The origin of classical reality in our quantum world is a long-standing mystery. Here, we examine a nitrogen vacancy center evolving naturally in the presence of its environment to study quantum Darwinism - the proliferation of information about preferred quantum states throughout the world via the environment. This redundantly imprinted information accounts for the perception of objective reality, as it is independently accessible by many without perturbing the system of interest. To observe the emergence of redundant information, we implement a novel dynamical decoupling scheme that enables …
Quantum-to-classical transition and the emergence of trajectory level Darwinism with measurements distributed in time: a path integral approach
Centre for Nano Science and Engineering, Indian Institute of Science（印度科学学院纳米科学与工程中心）；Department of Physics, Indian Institute of Technology Madras（印度理工学院马德拉斯分校物理系）；Center for Quantum Information, Communication and Computing, Indian Institute of Technology Madras（印度理工学院马德拉斯分校量子信息、通信与计算中心）；Instrumentation and Applied Physics, Indian Institute of Science（印度科学学院仪器与应用物理系）
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 o…
We critically examine the role that correlations established between a system and fragments of its environment play in characterising the ensuing dynamics. We employ a class of dephasing models where the state of the initial environment represents a tunable degree of freedom that qualitatively and quantitatively affects the correlation profiles, but nevertheless results in the same reduced dynamics for the system. We apply recently developed tools for the characterisation of non-Markovianity to carefully assess the role that correlations, as quantified by the (quantum) Jensen-Shannon divergenc…
Motivated by the advances of quantum Darwinism and recognizing the role played by redundancy in identifying the small subset of quantum states with resilience characteristic of objective classical reality, we explore the implications of redundant records for consistent histories. The consistent histories formalism is a tool for describing sequences of events taking place in an evolving closed quantum system. A set of histories is consistent when one can reason about them using Boolean logic, i.e., when probabilities of sequences of events that define histories are additive. However, the vast m…
