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

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—environment—induced superselection)—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 yet 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|2 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.

Classicality with(out) decoherence: Concepts, relation to Markovianity, and a random matrix theory approach

“…[35]. Furthermore, a topic which we will only briefly touch is quantum Darwinism [36,37], which further refines the notion of decoherence in OQS.…”

“…However, a refinement of this idea is possible and has lead to the recently much studied approach of quantum Darwinism, see Ref. [36,37] and references therein. In a nutshell, quantum Darwinism starts by dividing the bath into many different "fragments" F ⊂ B and asserts that most fragments, even those of small size, have (close) to zero quantum discord with respect to the pointer basis, i.e., Eq.…”

“…2. Notably, the role of multi-time statistics to probe the stability of pointer states and its connection to Markovianity has not yet been made in the literature on OQS decoherence [1][2][3][4], and it is also not the focus of quantum Darwinism [36,37]. It has been realized, however, in a numerical study of quantum Brownian motion that non-Markovianity hinders quantum Darwinism [51].…”

Non-Kolmogorovian Probabilities and Quantum Technologies

“…However, it is still hard to explain the probabilistic behavior and why one observes a discontinuous change of state during measurements. For an up-to-date exposition of the problems involved and the state of the art of the proposed solutions, see [ 47 , 48 ]. The very idea of describing a macroscopic system as a simple mereological sum of quantum microscopic parts interacting unitarily is rather ambitious.…”

Human Cognition Surpasses the Nonlocality Tsirelson Bound: Is Mind Outside of Spacetime?

“…We based our previous work on the premise that measurement and actualization, which creates the de initive classical world (this coincides with the contextuality-complementarity philosophy of Bohr 1 ) can happen only in a speci ic basis. However we still do not have a comprehensive theory for the emergence of a speci ic basis, except the recent attempts from Quantum Darwinism perspectives as proposed by Zurek (2022) in terms of de-coherence theory. We note that decoherence does not yield a speci ic basis.…”