Does Decoherence Select the Pointer Basis of a Quantum Meter?

The consensus regarding quantum measurements rests on two statements: (i) von Neumann’s standard quantum measurement theory leaves undetermined the basis in which observables are measured, and (ii) the environmental decoherence of the measuring device (the “meter”) unambiguously determines the measuring (“pointer”) basis. The latter statement means that the environment monitors (measures) selected observables of the meter and (indirectly) of the system. Equivalently, a measured quantum state must end up in one of the “pointer states” that persist in the presence of the environment. We find that, unless we restrict ourselves to projective measurements, decoherence does not necessarily determine the pointer basis of the meter. Namely, generalized measurements commonly allow the observer to choose from a multitude of alternative pointer bases that provide the same information on the observables, regardless of decoherence. By contrast, the measured observable does not depend on the pointer basis, whether in the presence or in the absence of decoherence. These results grant further support to our notion of Quantum Lamarckism, whereby the observer’s choices play an indispensable role in quantum mechanics.

Reference Frame Induced Symmetry Breaking on Holographic Screens

Any interaction between finite quantum systems in a separable joint state can be viewed as encoding classical information on an induced holographic screen. Here we show that when such an interaction is represented as a measurement, the quantum reference frames (QRFs) deployed to identify systems and pick out their pointer states induce decoherence, breaking the symmetry of the holographic encoding in an observer-relative way. Observable entanglement, contextuality, and classical memory are, in this representation, logical and temporal relations between QRFs. Sharing entanglement as a resource requires a priori shared QRFs.

Extragalactic neutrinos as tracers of dark matter?

Neutrinos produced in extragalactic sources may experience flavor-oscillations and decoherence on their way to Earth due to their interaction with dark matter (DM). As a result, they may be detected in pointer-states other than the flavor states produced at the source. The oscillation pattern and the structure of the pointer-states can give us information on the characteristics of the DM and the kind of interaction that has taken place. From this perspective, neutrinos can be viewed as DM-tracers. We study the local evolution of neutrino flavor-eigenstates due to local effects produced by the presence of DM. To explore the sensitivity of the model, we consider different DM density profiles, masses and interactions. Starting from the eigenstates of the neutrino mass Hamiltonian, we construct flavor-states with the neutrino mixing-matrix in vacuum. We then include local interactions with DM, acting along the neutrino path towards the Earth, and analyze the resulting probabilities. In doing so, we adopt different DM density profiles, e.g. a constant, a local isotropic, and a Navarro–Frenk–White density distribution. Finally, by following the time-evolution of the flavor-states, we identify pointer-states and interpret the results in terms of the adopted DM model. In addition, neutrinos may experience changes in the oscillation parameters and resonances (MSW effect), the extent of which depends on the DM density profile. Thus, the presence of DM may enhance or suppress the oscillation pattern. The suppression of components of the neutrino wave-packet (decoherence effects) may also take place. The features of the calculated response seem to support the notion that these neutrinos can be taken as DM tracers. From a theoretical point of view, the coexistence and/or competition of decoherence and matter effects is sustained by the results.

Quantum jumps, Born’s rule, and objective classical reality via quantum Darwinism

Emergence of the classical from the quantum substrate is a long-standing conundrum. The chapter describes its resolution based on three insights that stem from the recognition of the role of the environment. The chapter begins with the derivation of preferred states that define “events”, the essence of everyday classical reality. They arise from the tension between the unitary quantum dynamics and the nonlinear amplification inherent in replicating information. The resulting pointer states are consistent with these obtained via environment-induced superselection (einselection). They determine what can happen by defining events such as quantum jumps without appealing to Born’s rule for probabilities. Probabilities can be now deduced from envariance (a symmetry of entangled quantum states). With probabilities at hand one can quantify information flows accompanying decoherence. Effective amplification they represent explains perception of objective classical reality arising from within the quantum universe through redundancy of the pointer state records in their environment—through quantum Darwinism.

Quantum theory of the classical: quantum jumps, Born’s Rule and objective classical reality via quantum Darwinism

The emergence of the classical world from the quantum substrate of our Universe is a long-standing conundrum. In this paper, 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 the derivation of preferred sets of states that help to define what exists—our everyday classical reality. They emerge as a result of the 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 derivation is accomplished without the usual tools of decoherence, and accounts for the appearance of quantum jumps and the emergence of preferredpointer statesconsistent with those obtained via environment-induced superselection, oreinselection. The pointer states obtained in this way determine what can happen—define events—without appealing to Born’s Rule for probabilities. Therefore,pk=|ψk|2can now be deduced from the entanglement-assisted invariance, orenvariance—a symmetry of entangled quantum states. With probabilities at hand, one also gains new insights into the foundations of quantum statistical physics. Moreover, one can now analyse the information flows responsible for decoherence. These information flows explain how the perception of objective classical reality arises from the quantum substrate: the effective amplification that they represent accounts for the objective existence of the einselected states of macroscopic quantum systems through the redundancy of pointer state records in their environment—throughquantum Darwinism.This article is part of a discussion meeting issue ‘Foundations of quantum mechanics and their impact on contemporary society’.

Decoherence and pointer states in small antiferromagnets: A benchmark test

We study the decoherence process of a four spin-1/2 antiferromagnet that is coupled to an environment of spin-1/2 particles. The preferred basis of the antiferromagnet is discussed in two limiting cases and we identify two exact pointer states. Decoherence near the two limits is examined whereby entropy is used to quantify the robustness of states against environmental coupling. We find that close to the quantum measurement limit, the self-Hamiltonian of the system of interest can become dynamically relevant on macroscopic timescales. We illustrate this point by explicitly constructing a state that is more robust than (generic) states diagonal in the system-environment interaction Hamiltonian.

An Algebraic Approach to Unital Quantities and their Measurement

The goals of this paper fall into two closely related areas. First, we develop a formal framework for deterministic unital quantities in which measurement unitization is understood to be a built-in feature of quantities rather than a mere annotation of their numerical values with convenient units. We introduce this idea within the setting of certain ordered semigroups of physical-geometric states of classical physical systems. States are assumed to serve as truth makers of metrological statements about quantity values. A unital quantity is presented as an isomorphism from the target system’s ordered semigroup of states to that of positive reals. This framework allows us to include various derived and variable quantities, encountered in engineering and the natural sciences. For illustration and ease of presentation, we use the classical notions of length, time, electric current and mean velocity as primordial examples. The most important application of the resulting unital quantity calculus is in dimensional analysis. Second, in evaluating measurement uncertainty due to the analog-to-digital conversion of the measured quantity’s value into its measuring instrument’s pointer quantity value, we employ an ordered semigroup framework of pointer states. Pointer states encode the measuring instrument’s indiscernibility relation, manifested by not being able to distinguish the measured system’s topologically proximal states. Once again, we focus mainly on the measurement of length and electric current quantities as our motivating examples. Our approach to quantities and their measurement is strictly state-based and algebraic in flavor, rather than that of a representationalist-style structure-preserving numerical assignment.