We examine the emergence and suppression of signatures of quantum Darwinism when the system of interest interacts with a complex, structured environment. We introduce an extended spin-star model where the system is coupled to $N$ independent spin-chains. Each site of the chain then lives in a definite layer of the environment, and hence we term this the "onion" model. We fix the system-environment interaction such that classical objectivity is guaranteed if the environment consists of a single layer. Considering a fully factorized initial state for all constituent sub-systems, we then examine how the emergence and proliferation of signatures of quantum Darwinism are delicately dependent on the chain interaction, establishing that when the chains are considered as indivisible fragments to be interrogated, characteristic redundancy plateaux are always observed at least transiently. In contrast, observing a redundant encoding in a specific layer is highly sensitive to the nature of the interaction. Finally, we consider the case in which each chain is initialized in the ground state of the interaction Hamiltonian, establishing that this case shares the qualitative features of the factorized initial state case, however now the strength of the applied magnetic field has a significant impact on whether quantum Darwinism can be observed. We demonstrate that the presence or absence of quantum Darwinistic features can be understood by analysing the correlations within a layer using total mutual information and global quantum discord.
Quantum system interacting with environment can induce redundant encoding of the information of system into a multipartite environment, which is the essence of quantum Darwinism. At the same time, environment may scramble the initially localized information about the system. We mainly investigate the relevance between information scrambling in environment and the emergence of quantum Darwinism. First, we generally identify that when the system shows a Darwinistic behavior system information that is initially localized in the environment is not scrambled, while when Darwinism disappears scrambl…
We study quantum Darwinism--the redundant recording of information about the preferred states of a decohering system by its environment--for an object illuminated by a black body. In the cases of point-source and isotropic illumination, we calculate the quantum mutual information between the object and its photon environment. We demonstrate that this realistic model exhibits fast and extensive proliferation of information about the object into the environment and results in redundancies orders of magnitude larger than the exactly soluble models considered to date.
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 non interacting 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 {\it a' la} quantum Darwinism needs to be fully understood. We study a model of local interaction between a simple quantum system and a multi-mode environment that allows for a clear investigation…
We examine the emergence of objectivity via quantum Darwinism through the use of a collision model, i.e. where the dynamics is modeled through sequences of unitary interactions between the system and the individual constituents of the environment, termed "ancillas". By exploiting versatility of this framework, we show that one can transition from a "Darwinistic" to an "encoding" environment by simply tuning their interaction. Furthermore we establish that in order for a setting to exhibit quantum Darwinism we require a mutual decoherence to occur between the system and environmental ancillas, …
In quantum Darwinism, the pointer observable of a system leaves redundant imprints in its environment after decoherence. Each imprint is recorded in a fraction of the environment, which identifies a particular partition of the environment. An ambiguity situation may occur when another observable noncommuting to the pointer observable also leaves redundant imprints with respect to another partition of the environment. We study this problem based on a uniqueness theorem we proved. We find that within a particular subset of all possible partitions of the environment, the observable of the system …
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.
Quantum Darwinism recognizes that we - the observers - acquire our information about the "systems of interest" indirectly from their imprints on the environment. Here, we show that information about a system can be acquired from a mixed-state, or hazy, environment, but the storage capacity of an environment fragment is suppressed by its initial entropy. In the case of good decoherence, the mutual information between the system and the fragment is given solely by the fragment's entropy increase. For fairly mixed environments, this means a reduction by a factor 1-h, where h is the haziness of th…
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…
We study the behavior of Quantum Darwinism (Zurek, [8]) within the iterative, random unitary operations qubit-model of pure decoherence (Novotny et al, [6]). We conclude that Quantum Darwinism, which describes the quantum mechanical evolution of an open system S from the point of view of its environment E, is not a generic phenomenon, but depends on the specific form of input states and on the type of S-E-interactions. Furthermore, we show that within the random unitary model the concept of Quantum Darwinism enables one to explicitly construct and specify artificial input states of environment…
In this Letter we investigate Quantum Darwinism and the emergence of a classical world from the quantum one in connection with the spectral properties of the environment. We use a microscopic model of quantum environment in which, by changing a simple system parameter, we can modify the information back flow from environment into the system, and therefore its non-Markovian character. We show that the presence of memory effects hinders the emergence of classical objective reality. We conjecture that this phenomenon is connected to the absence of a measurement-scheme interpretation for quantum t…
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 …
Quantum Darwinism and spectrum broadcast structure describe the emergence of objectivity in quantum systems. However, it is unclear whether these two frameworks lead to consistent predictions on the objectivity of the state of a quantum system in a given scenario. In this paper, we jointly investigate quantum Darwinism and spectrum broadcasting, as well as the subdivision of quantum Darwinism into accessible information and quantum discord, in a two-level system interacting with an $N$-level environment via a random matrix coupling. We propose a novel partial trace method to suitably and consi…
Quantum-to-classical transition is a fundamental open question in physics frontier. Quantum decoherence theory points out that the inevitable interaction with environment is a sink carrying away quantum coherence, which is responsible for the suppression of quantum superposition in open quantum system. Recently, quantum Darwinism theory further extends the role of environment, serving as communication channel, to explain the classical objectivity emerging in quantum measurement process. Here, we used a six-photon quantum simulator to investigate classical and quantum information proliferation …
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…
We combine the collisional picture for open system dynamics and the control of the rate of decoherence provided by the quantum (anti-)Zeno effect to illustrate the temporal unfolding of the redundant encoding of information into a multipartite environment that is at the basis of Quantum Darwinism, and to control it. The rate at which such encoding occurs can be enhanced or suppressed by tuning the dynamical conditions of system-environment interaction in a suitable and remarkably simple manner. This would help the design of a new generation of quantum experiments addressing the elusive phenome…
We investigate the influence of dissipation and decoherence on quantum Darwinism by generalizing Zurek's original qubit model of decoherence and the establishment of pointer states (Zurek, Nature Physics 5, 181 - 188 (2009)). Our model allows for repeated multiple qubit-qubit couplings between system and environment which are described by randomly applied two-qubit quantum operations inducing entanglement, dissipation and dephasing. The resulting stationary qubit states of system and environment are investigated. They exhibit the intricate influence of entanglement generation, dissipation and …
We study quantum Darwinism, the redundant recording of information about the preferred states of a decohering system by its environment, for an object illuminated by a blackbody. We calculate the quantum mutual information between the object and its photon environment for blackbodies that cover an arbitrary section of the sky. In particular, we demonstrate that more extended sources have a reduced ability to create redundant information about the system, in agreement with previous evidence that initial mixedness of an environment slows---but does not stop---the production of records. We also s…
Quantum Darwinism describes the proliferation, in the environment, of multiple records of selected states of a quantum system. It explains how the fragility of a state of a single quantum system can lead to the classical robustness of states of their correlated multitude; shows how effective `wave-packet collapse' arises as a result of proliferation throughout the environment of imprints of the states of quantum system; and provides a framework for the derivation of Born's rule, which relates probability of detecting states to their amplitude. Taken together, these three advances mark consider…
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 describes objectivity of quantum systems via their correlations with their environment--information that hypothetical observers can recover by measuring the environments. However, observations are done with respect to a frame of reference. Here, we take the formalism of [Giacomini, Castro-Ruiz, & Brukner. Nat Commun 10, 494 (2019)], and consider the repercussions on objectivity when changing quantum reference frames. We find that objectivity depends on non-degenerative relative separations, conditional state localisation, and environment macro-fractions. There is different ob…
We report on an experimental assessment of the emergence of Quantum Darwinism (QD) from engineered open-system dynamics. We use a photonic hyperentangled source of graph states to address the effects that correlations among the elements of a multi-party environment have on the establishment of objective reality ensuing the quantum-to-classical transition. Besides embodying one of the first experimental efforts towards the characterization of QD, our work illustrates the non-trivial consequences that multipartite entanglement and, in turn, the possibility of having environment-to-system back-ac…
Quantum non Markovianity and quantum Darwinism are two phenomena linked by a common theme: the flux of quantum information between a quantum system and the quantum environment it interacts with. In this work, making use of a quantum collision model, a formalism initiated by Sudarshan and his school, we will analyse the efficiency with which the information about a single qubit gained by a quantum harmonic oscillator, acting as a meter, is transferred to a bosonic environment. We will show how, in some regimes, such quantum information flux is inefficient, leading to the simultaneous emergence …
Quantum Darwinism is a compelling theory that describes the quantum-to classical transition as the emergence of objectivity of quantum systems. Spectrum broadcast structure and strong quantum Darwinism are two extensions of this theory with emphasis on state structure and information respectively. The complete experimental verification of these three frameworks, however, requires quantum state tomography over both the system and accessible environments, thus limiting the feasibility and scalability of experimental tests. Here, we introduce a subspace-dependent objectivity operation and constru…
It is well-known that decoherence is a crucial barrier in realizing various quantum information processing tasks; on the other hand, it plays a pivotal role in explaining how a quantum system's fragile state leads to the robust classical state. Zurek [Nat. Phys. 5, 181-188 (2009)] has developed the theory which successfully describes the emergence of classical objectivity of quantum system via decoherence, introduced by the environment. Here, we consider two systems for a model universe, in which the first system shows a random quantum state, and the other represents the environment. We take 2…
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…
The objective, classical world emerges from the underlying quantum substrate via the proliferation of redundant copies of selected information into the environment, which acts as a communication channel, transmitting that information to observers. These copies are independently accessible, allowing many observers to reach consensus about the state of a quantum system via its imprints in the environment. Quantum Darwinism recognizes that the redundancy of information is thus central to the emergence of objective reality in the quantum world. However, in addition to the "quantum system of intere…
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, E, is in a non-ideal (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, S, and an environment fragment, F, is given so…
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 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）
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…
A state selected at random from the Hilbert space of a many-body system is overwhelmingly likely to exhibit highly non-classical correlations. For these typical states, half of the environment must be measured by an observer to determine the state of a given subsystem. The objectivity of classical reality-the fact that multiple observers can agree on the state of a subsystem after measuring just a small fraction of its environment-implies that the correlations found in nature between macroscopic systems and their environments are very exceptional. Building on previous studies of quantum Darwin…
"How much information about a system $\mathcal{S}$ can one extract from a fragment $\mathcal{F}$ of the environment $\mathcal{E}$ that decohered it?" is the central question of Quantum Darwinism. To date, most answers relied on the quantum mutual information of $\mathcal{SF}$, or on the Holevo bound on the channel capacity of $\mathcal{F}$ to communicate the classical information encoded in $\mathcal{S}$. These are reasonable upper bounds on what is really needed but much harder to calculate -- the accessible information in the fragment $\mathcal{F}$ about $\mathcal{S}$. We consider a model ba…
In a recent Letter [Phys. Rev. Lett. 122, 010403 (2019)], an equivalence is proposed between the so-called Spectrum Broadcast Structure for a system-multienvironment quantum state, and the conjunction of two information-theory notions: (a) Strong Quantum Darwinism; and (b) Strong Independence. Here, we show that the mathematical formulation of condition (b) by the authors (namely, the pairwise independence of the fragments of the environment, conditioned on the system), is necessary but not sufficient to ensure the equivalence. We propose a simple counter-example, together with a strengthened …
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…
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…
Quantum mechanics is one of the most successful theories, correctly predicting huge class of physical phenomena. Ironically, in spite of all its successes, there is a notorious problem: how does Nature create a ''bridge'' from fragile quanta to the robust, objective world of everyday experience? It is now commonly accepted that the most promising approach is the Decoherence Theory, based on the system-environment paradigm. To explain the observed redundancy and objectivity of information in the classical realm, Zurek proposed to divide the environment into independent fractions and argued that…
Quantum darwinism (QD) is the process responsible for the proliferation of redundant information in the environment of a quantum system that is being decohered. This enables independent observers to access separate environmental fragments and reach consensus about the system's state. In this work, we study the effect of disorder in the emergence of QD and find that a highly disordered environment is greatly beneficial for it. By introducing the notion of lack of redundancy to quantify objectivity, we show that it behaves analogously to the entanglement entropy (EE) of the environmental eigenst…
Emergence of the classical world from the quantum substrate of our Universe is a long-standing conundrum. I describe three insights into the transition from quantum to classical that are based on the recognition of the role of the environment. I begin with derivation of preferred sets of states that help define what exists - our everyday classical reality. They emerge as a result of breaking of the unitary symmetry of the Hilbert space which happens when the unitarity of quantum evolutions encounters nonlinearities inherent in the process of amplification - of replicating information. This der…
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…
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…
We study quantum Darwinism -- the redundant recording of information about a decohering system by its environment -- in zero-temperature quantum Brownian motion. An initially nonlocal quantum state leaves a record whose redundancy increases rapidly with its spatial extent. Significant delocalization (e.g., a Schroedinger's Cat state) causes high redundancy: many observers can measure the system's position without perturbing it. This explains the objective (i.e. classical) existence of einselected, decoherence-resistant pointer states of macroscopic objects.
Quantum Darwinism recognizes the role of the environment as a communication channel: Decoherence can selectively amplify information about the pointer states of a system of interest (preventing access to complementary information about their superpositions) and can make records of this information accessible to many observers. This redundancy explains the emergence of objective, classical reality in our quantum Universe. Here, we demonstrate that the amplification of information in realistic spin environments can be quantified by the quantum Chernoff information, which characterizes the distin…
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）
Quantum systems interacting with environments tend to have their information lost from transmission through the correlations generated with the degrees of freedom of the environment. For situations where we have non- Markovian environments, the information contained in the environment may return to the system and such effect can be captured by non-Markovian witnesses. In the present work, we use a central qubit coupled to a spin chain with Ising interactions subject to a magnetic field, i.e., a central spin model, and solve the exact dynamics of a system subject to dephasing dynamics via Kraus…
We report an experiment that uses the environmental selection, a key concept in the recent theory of quantum Darwinism, as a mechanism to realize the entanglement filter, a useful quantum information device that filters out certain entangled states. In the experiment, the environment of two qubits is controlled to favor an entangled state and kill other competing components in the input state. The initial state has vanishing entanglement, but the state surviving after interaction with the environment is close to a maximally entangled state, with an entanglement fidelity of $(94.7\pm 1.9)%$ mea…
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…
