**Contents**



#### **Preface to "Quantum Darwinism and Friends"**

Wojciech Hubert Zurek has made seminal contributions to several areas of theoretical physics. This includes decoherence, where he had the key insight that physical environments superselect certain "pointer" states, and the foundations of quantum and classical information (e.g., the no-cloning theorem and quantum discord). His work on the dynamics of non-equilibrium phase transitions led to the Kibble–Zurek mechanism. Quantum Darwinism—the subject of this volume—is a culmination of advances that started with decoherence. It accounts for the emergence of objective classical reality in our quantum universe.

Wojciech Zurek earned his MSc in Krakow, in his native Poland, and his PhD at the University of Texas at Austin, where he remained until 1981 as a postdoctoral fellow of John Archibald Wheeler. In 1981, Zurek joined the group of Kip Thorne at Caltech as a Tolman Fellow and arrived at Los Alamos in 1984 as an Oppenheimer Fellow. He rose to the position of group leader of the Theoretical Astrophysics Group in 1991. In 1996, Zurek was named Laboratory Fellow of the Theory Division.

In his long career, Wojciech Zurek has won many honors and awards. A non-comprehensive list includes the Phi Beta Kappa Visiting Lecturer (2004), the Alexander von Humboldt Prize (2005), the Marian Smoluchowski Medal (2009), the Albert Einstein Professorship (awarded in 2010 by the Ulm University), the Order of Polonia Restituta (2012), and the Los Alamos Medal (2014).

How many of us have heard, or maybe even made, the statement that "quantum mechanics is weird"? As human beings that evolved at classical energy and lengths scales, we are so used to the fact that things look "classical" that the actual workings of our quantum Universe constantly have us in awe, confuse us, and sometimes even appall us.

Take, for instance, the frequently maltreated cat. If any two of us look at the same cat, we will both conclude that we are looking at a cat. Well, actually, we conclude that we both "perceive" a cat, and we will agree about its state of well-being. From a fundamental point of view, the question has to be: why? The answer originates in the fact that any fraction of photons that we intercept with our eyes carries the same, classical information about the lovely beast. The more formal analysis of the emergence of this classical objectivity is known as Quantum Darwinism, as it relies on Darwinian fitness of certain states—their ability to not just survive immersion in the environment, but create, multiple "offspring" of the information about themselves in the photon (and other) environments, where they can be accessed by observers such as us.

Quantum Darwinism shows how the perception of objective classical reality arises via selective amplification and the spreading of information in our fundamentally quantum universe. Quantum Darwinism goes beyond decoherence, as it recognizes that the many copies of the system's pointer states are imprinted on the environment: agents acquire data indirectly, by intercepting environment fragments (rather than directly measuring systems of interest). The data disseminated through the environment provide us with shared information about stable, effectively classical pointer states. Humans rely primarily on the photon environment, eavesdropping on "objects of interest" by intercepting tiny fractions of photons that contributed to decoherence.

In essence, Zurek has taught us nothing short of understanding why our world looks classical, despite the fact that our Universe is quantum to the core. This special issue collected a wide range of recent contributions motivated and inspired by Zurek's work all leveraging in one way or another the power of quantum correlations and their ephemeral nature.

#### **Sebastian Deffner, Raymond Laflamme, Juan Pablo Paz, and Michael Zwolak** *Editors*

### *Review* **Quantum Theory of the Classical: Einselection, Envariance, Quantum Darwinism and Extantons**

**Wojciech Hubert Zurek**

> Theory Division, Mail Stop B213, LANL, Los Alamos, NM 87545, USA

**Abstract:** 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. This approach shares with the Relative State Interpretation of Everett the view that collapse of the wavepacket reflects perception of the state of the rest of the Universe *relative* to the state of observer's records. However, our "let quantum be quantum" approach poses questions absent in Bohr's Copenhagen Interpretation that relied on the preexisting classical domain. Thus, one is now forced to seek preferred, predictable, hence effectively classical but ultimately quantum states that allow observers keep reliable records. Without such *(i) preferred basis* relative states are simply "too relative", and the ensuing *basis ambiguity* makes it difficult to identify events (e.g., measurement outcomes). Moreover, universal validity of quantum theory raises the issue of *(ii) the origin of Born's rule*, *pk* = |*ψk*|2, relating probabilities and amplitudes (that is simply postulated in textbooks). Last not least, even preferred pointer states (defined by *einselection*—*<sup>e</sup>*nvironment—*in*duced super*selection*)— are still quantum. Therefore, unlike classical states that exist objectively, quantum states of an individual system cannot be found out by an initially ignorant observer through direct measurement without being disrupted. So, to complete the 'quantum theory of the classical' one must identify *(iii) quantum origin of objective existence* and explain how the information about objectively existing states can appear to be essentially inconsequential for them (as it does for states in Newtonian physics) and ye<sup>t</sup> matter in other settings (e.g., thermodynamics). I show how the mathematical structure of quantum theory supplemented by the only uncontroversial measurement postulate (that demands immediate repeatability—hence, predictability) leads to preferred states. These *(i) pointer states* correspond to measurement outcomes. Their stability is a prerequisite for objective existence of effectively classical states and for events such as quantum jumps. Events at hand, one can now enquire about their probability—the probability of a pointer state (or of a measurement record). I show that the symmetry of entangled states—*(ii) entanglement—assisted invariance* or *envariance*—implies Born's rule. Envariance also accounts for the loss of phase coherence between pointer states. Thus, decoherence can be traced to symmetries of entanglement and understood without its usual tool—reduced density matrices. A simple and manifestly noncircular derivation of *pk* = |*ψk*|<sup>2</sup> follows. Monitoring of the system by its environment in course of decoherence typically leaves behind multiple copies of its pointer states in the environment. Only pointer states can survive decoherence and can spawn such plentiful information-theoretic progeny. This *(iii) quantum Darwinism* allows observers to use *environment as a witness*—to find out pointer states indirectly, leaving systems of interest untouched. Quantum Darwinism shows how epistemic and ontic (coexisting in *epiontic* quantum state) separate into robust objective existence of pointer states and detached information about them, giving rise to *extantons*—composite objects with system of interest in the core and multiple records of its pointer states in the halo comprising of environment subsystems (e.g., photons) which disseminates that information throughout the Universe.

**Keywords:** decoherence; einselection; quantum jumps; Born's rule; envariance; quantum Darwinism; quantum-classical transition; existential interpretation; extantons

**Citation:** Zurek, W.H. Quantum Theory of the Classical: Einselection, Envariance, Quantum Darwinism and Extantons. *Entropy* **2022**, *24*, 1520. https://doi.org/10.3390/e24111520

Academic Editor: Ronnie Kosloff

Received: 6 December 2021 Accepted: 21 March 2022 Published: 24 October 2022

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