Spectrum Broadcast Structure Research Articles

The meaning of redundancy and consensus in quantum objectivity

While the terms "redundancy" and "consensus" are often used as synonyms in the context of quantum objectivity, we show here that these should be understood as two related but distinct notions, that quantify different features of the quantum-to-classical transition. We show that the two main frameworks used to measure quantum objectivity, namely spectrum broadcast structure and quantum Darwinism, are best suited to quantify redundancy and consensus, respectively. Furthermore, by analyzing explicit examples of states with nonlocally encoded information, we highlight the potentially stark difference between the degrees of redundancy and consensus. In particular, this causes a break in the hierarchical relations between spectrum broadcast structure and quantum Darwinism. Our framework provides a new perspective to interpret known and future results in the context of quantum objectivity, paving the way for a deeper understanding of the emergence of classicality from the quantum realm.

Composite Discordant States and Quantum Darwinism.

The framework of Quantum Darwinism strives at characterizing the quantum-to-classical transition by introducing the concept of redundancy of information-as measured by Mutual Information-that a set of observers would acquire on the state of a physical system of interest. Further development on this concept, in the form of Strong Quantum Darwinism and Spectrum Broadcast Structures, has recently led to a more fine-grained identification of the nature of such information, which should not involve any quantum correlations between observing and observed systems, while the assessment of information proliferation from individual systems has attracted most of the attention so far, the way such mechanism takes place in more complex states is open to exploration. To this end, we shall consider a two-qubit state, sharing initial quantum correlations in the form of Quantum Discord, and different dephasing-like interactions between them and an observing environment. We will focus on the amount of information regarding the subsystem not involved in the interaction that is proliferated to the environment. We shall refer to this as mediated redundancy. We will show that, in some cases, the channel capacity of the subsystems, given these interactions, can exceed that of the fragments.

Non-Perfect Propagation of Information to a Noisy Environment with Self-Evolution.

We study the non-perfect propagation of information for evolving a low-dimensional environment that includes self-evolution as well as noisy initial states and analyse the interrelations between the degree of objectivization and environment parameters. In particular, we consider an analytical model of three interacting qubits and derive its objectivity parameters. The numerical analysis shows that the quality of the spectrum broadcast structure formed during the interaction may exhibit non-monotonicity both in the speed of self-dynamics of the environment as well as its mixedness. The former effect is particularly strong, showing that—considering part of the environment as a measurement apparatus—an increase of the external magnetic field acting on the environment may turn the vague measurement into close to ideal. The above effects suggest that quantum objectivity may appear after increasing the dynamics of the environment, although not with respect to the pointer basis, but some other, which we call the generalized pointer or indicator basis. Furthermore, it seems also that, when the objectivity is poor, it may be improved, at least by some amount, by increasing the thermal noise. We provide further evidence of this by analysing the upper bounds on distance to the set of states representing perfect objectivity in the case of a higher number of qubits.

Roads to objectivity: Quantum Darwinism, Spectrum Broadcast Structures, and Strong quantum Darwinism – a review

The problem of objectivity, i.e. how to explain on quantum grounds the objective character of the macroscopic world, is one of the aspects of the celebrated quantum-to-classical transition. Initiated by W. H. Zurek and collaborators, this problem gained some attention recently with several approaches being developed. The aim of this work is to compare three of them: quantum Darwinism, Spectrum Broadcast Structures, and strong quantum Darwinism. The paper is concentrated on foundations, providing a synthetic analysis of how the three approaches realize the idea of objectivity and how they are related to each other. As a byproduct of this analysis, a proof of a generalized Spectrum Broadcast Structure theorem is presented. Recent quantum Darwinism experiments are also briefly discussed.

Decoherence and objectivity in higher spin environments

We analyze decoherence and objectivization processes in spin-spin models for arbitrary spins. We first derive the most general analytic form of the decoherence factor in the measurement limit, where the interaction Hamiltonian dominates the rest. We then analyze thermal environments and derive exact, analytic formulas for both the decoherence factor and the state fidelity of post-interaction environment states. This allows to analyze the objectivization process of the state of the central spin during the interaction. We do so using, so called, Spectrum Broadcast Structures (SBS), which are specific multipartite quantum states encoding a certain operation notion of objectivity. We analyze analytically (for short times) and numerically how higher spin influences the efficiency of decoherence and objectivization processes. As expected, the higher the spin of the environment, the more efficient decoherence and objectivization become. This work is a generalization of previous studies, limited to spin-$1/2$ systems only, and we hope will be useful in future objectivity experiments.

Universal structure of objective states in all fundamental causal theories

A crucial question is how objective and classical behavior arises from a fundamental physical theory. Here we provide a natural definition of a decoherence process valid in all causal theories and show how its behavior can be extremely different from the quantum one. Remarkably, despite this, we prove that the so-called spectrum broadcast structure characterizes all objective states in every fundamental causal theory, exactly as in quantum mechanics. Our results show a stark contrast between the extraordinarily diverse decoherence behavior and the universal features of objectivity.

Comment on “Strong Quantum Darwinism and Strong Independence Are Equivalent to Spectrum Broadcast Structure”

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 formulation of condition (b), ensuring the equivalence proposed by the authors.

Appearance of objectivity for NV centers interacting with dynamically polarized nuclear environment

Quantum-to-classical transition still eludes a full understanding. Out of its multiple aspects, one has recently gained an increased attention—the appearance of objective world out of the quantum. One particular idea is that objectivity appears thanks to specific quantum state structures formation during the evolution, known as spectrum broadcast structures (SBS). Despite that quite some research was already performed on this strong and fundamental form of objectivity, the practical realization of SBS in a concrete physical medium has not been explicitly analyzed so far. In this work, we study the possibility to simulate objectivization process via SBS formation using widely studied nitrogen-vacancy centers in diamonds. Assuming achievable limits of dynamical polarization technique, we show that for high, but experimentally viable polarizations (p > 0.5) of nuclear spins and for magnetic fields lower than ≈20 G the state of the NV center and its nearest polarized environment approaches an SBS state reasonably well.

Witnessing non-objectivity in the framework of strong quantum Darwinism

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 construct a witness that detects non-objectivity by comparing the dynamics of the system-environment state with and without the objectivity operation. We then propose a photonic experimental simulation that implements the witnessing scheme. Our work proposes a route to further experimental exploration of the quantum to classical transition.

Glimpse of objectivity in bipartite systems for nonentangling pure dephasing evolutions

We study separable system-environment evolutions of pure dephasing type in the context of objectivity. We find that it can lead to the natural emergence of spectrum broadcast structures (SBSs), but at discrete time instances. Contrary to the standard way of obtaining SBS states, which requires entanglement, reaching such states here does not require decoherence (no unobserved environments are necessary). Yet the biggest difference is the basis with respect to which the SBS states are formed. Here it is not the pointer basis of the system given by the interaction with the environment, but their equal superposition basis, the so-called mutually unbiased basis. The price to pay is a simple SBS structure with just one environment and its momentary character.

Reexamination of the decoherence of spin registers

We revisit decoherence process of a qubit register interacting with a thermal bosonic bath. We generalize the previous studies by considering not only the register's behavior but also of a part of its environment. In particular, we are interested in information flow from the register to the environment, which we describe using recently introduced multipartite quantum state structures called Spectrum Broadcast Structures. Working in two specific cases of: i) two-qubit register and ii) collective decoherence, we identify the regimes where the environment acquires almost complete information about the register state. We also study in more detail the interesting causal aspects, related to the finite propagation time of the field disturbances between the qubits. Finally, we describe quantum state structures which appear due to the presence of protected spaces.

Strong Quantum Darwinism and Strong Independence are Equivalent to Spectrum Broadcast Structure.

How the objective everyday world emerges from the underlying quantum behavior 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 broadcast structure when combined with strong independence of the subenvironments. We further show that strong quantum Darwinism is sufficient and necessary to signal state objectivity without the requirement of strong independence. Our Letter unveils the deep connection between strong quantum Darwinism and spectrum broadcast structure, thereby making fundamental progress toward understanding and solving the emergence of classicality from the quantum world. Together they provide us a sharper understanding of the transition in terms of state structure, geometry, and quantum and classical information.

Objectivity (or lack thereof): Comparison between predictions of quantum Darwinism and spectrum broadcast structure

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 consistently partition the effective $N$-level environment, and compare the predictions with those obtained using the partitioning method proposed by Perez [Phys. Rev. A 81, 052326 (2010)]. We find that Quantum Darwinism can apparently emerge under the Perez trace even when spectrum broadcast structure does not emerge, and the majority of the quantum mutual information between system and environment fractions is in fact quantum in nature. This work therefore shows there can be discrepancies between quantum Darwinism, and the nature of information and spectrum broadcast structure.

Redundant information encoding in QED during decoherence

Decoherence processes in quantum electrodynamics due to neglecting either the radiation [L. Landau, Z. Phys. 45, 430 (1927)] or the charged matter [N. Bohr and L. Rosenfeld, K. danske vidensk. Selsk, Math.-Fys. Medd. XII, 8 (1933)] have been studied from the dawn of the theory. However what happens in between, when a part of the radiation may be observed, as is the case in many real-life situations, has not been analyzed yet. We present such an analysis for a non-relativistic, point-like charge and thermal radiation. In the dipole approximation, we solve the dynamics and show that there is a regime where, despite of the noise, the observed field carries away almost perfect and hugely redundant information about the charge momentum. We analyze a partial charge-field state and show that it approaches a so called spectrum broadcast structure.

Objectivity in the non-Markovian spin-boson model

Objectivity constitutes one of the main features of the macroscopic classical world. An important aspect of the quantum-to-classical transition issue is to explain how such a property arises from the microscopic quantum world. Recently, within the framework of open quantum systems, there has been proposed such a mechanism in terms of the, so-called, Spectrum Broadcast Structures. These are multipartite quantum states of the system of interest and a part of its environment, assumed to be under an observation. This approach requires a departure from the standard open quantum systems methods, as the environment cannot be completely neglected. In the present work we study the emergence of such a state-structures in one of the canonical models of the condensed matter theory: Spin-boson model, describing the dynamics of a two-level system coupled to an environment made up by a large number of harmonic oscillators. We pay much attention to the behavior of the model in the non-Markovian regime, in order to provide a testbed to analyze how the non-Markovian nature of the evolution affects the surfacing of a spectrum broadcast structure.

Analytical studies of spectrum broadcast structures in quantum Brownian motion

Spectrum broadcast structures are a new and fresh concept in the quantum-to-classical transition, introduced recently in the context of decoherence and the appearance of objective features in quantum mechanics. These are specific quantum state structures, responsible for the objectivization of the decohered state of a system. Recently, they have been demonstrated by means of the well-known quantum Brownian motion model of the recoilless limit (infinitely massive central system), as the principal interest lies in information transfer from the system to the environment. However, a final analysis relied on numerics. Here, after a presentation of the main concepts, we perform analytical studies of the model, showing the timescales and the efficiency of the spectrum broadcast structure formation. We consider a somewhat simplified environment, being random with a uniform distribution of frequencies.

Dynamical objectivity in quantum Brownian motion

Classical objectivity as a property of quantum states —a view proposed to explain the observer-independent character of our world from quantum theory, is an important step in bridging the quantum-classical gap. It was recently derived in terms of spectrum broadcast structures for small objects embedded in noisy photon-like environments. However, two fundamental problems have arisen: a description of objective motion and applicability to other types of environments. Here we derive an example of objective states of motion in quantum mechanics by showing the formation of dynamical spectrum broadcast structures in the celebrated, realistic model of decoherence —Quantum Brownian Motion. We do it for realistic, thermal environments and show their noise-robustness. This opens a potentially new method of studying the quantum-to-classical transition.

Objectivisation In Simplified Quantum Brownian Motion Models

Birth of objective properties from subjective quantum world has been one of the key questions in the quantum-to-classical transition. Basing on recent results in the field, we study it in a quantum mechanical model of a boson-boson interaction-quantum Brownian motion. Using various simplifications we prove a formation for thermal environments of, so called, spectrum broadcast structures, responsible for perceived objectivity. In the quantum measurement limit we prove that this structure is always formed, providing the characteristic timescales. Including self-Hamiltonians of the environment, we show the exponential scaling of the effect with the size of the environment. Finally, in the full model we numerically study the influence of squeezing in the initial state of the environment, showing broader regions of formation than for non-squeezed thermal states.