This paper explores the possibility that linear dynamical maps might be used to describe the energy-conserving, entropy-increasing motions which occur in closed thermodynamic systems as they approach canonical thermal equilibrium. ForN-level quantum systems withN>2, we prove that no such maps exist which are independent of the initial state.

The identification of a set of mutually exclusive and exhaustive propositions concerning the states of quantum systems is a corner stone of the information-theoretic foundations of quantum statistics; but the set which is conventionally adopted is in fact incomplete, and is customarily deduced from numerous misconceptions of basic quantum mechanical principles. This paper exposes and corrects these common misstatements. It then identifies a new set of quantum state propositions which is truly exhaustive and mutually exclusive, and which is compatible with (...) the foundations of quantum theory. (shrink)

When the state of a physical system is not fully determined by available data, it should be possible nevertheless to make a systematic guess concerning the unknown state by applying the principles of information theory. The resulting theoretical blend of informational and mechanical constructs should then constitute a modern structure for statistical physics. Such a program has been attempted by a number of authors, most notably Jaynes, with seeming success. However, we demonstrated in a recent publication that the standard list (...) of so-called “mutually exclusive and exhaustive” quantum states that is commonly employed by these authors is in fact not exhaustive. It follows that the information-theoretic foundations of quantum statistics must be reformulated. The present paper discusses the fundamental problems involved and establishes a format for the correct application of information theory to quantum mechanical situations. (shrink)

An interpretation of quantum mechanics that rejects hidden variables has to say something about the way measurement can be understood as a transformation on states of individual systems, and that leads to the core of the interpretive problems posed by Luders' projection rule: What, if any, is its physical content? In this paper I explore one suggestion which is implicit in usual interpretations of the rule and show that this view does not stand on solid ground. In the process, important (...) aspects of the role played by the projection postulate in the conceptual structure of quantum mechanics will be clarified. It will be shown in particular that serious objections can be raised against the (often implicit) view that identifies the physical relation of compatibility preserved by Luders' rule with the relation of simultaneous measurability. (shrink)

We analyze the question whether or not quantum theory should be used to describe single particles. Our final result is that a rational basis for such an ’individuality interpretation’ does not exist. A critical examination of three principles, supporting the individuality interpretation, leads to the result that no one of these principles seems to be realized in nature. The well-known controversy characterized by the names of Einstein, Bohr and Bell is analyzed. EPR proved ’predictive incompleteness’ of quantum theory, which implies (...) that no individuality interpretation exists. Contrary to the common opinion, Bell’s proof of ’metaphysical completeness’ does not invalidate EPR’s proof because two crucially different meanings of ’completeness’ are involved. The failure to distinguish between these two meanings is closely related to a fundamentally deterministic world view, which dominated the thinking of the 19th century and determines our thinking even today. (shrink)

It is shown that the physics and semantics of quantum measurement provide a natural interpretation of the weak neighborhoods of the states on observable algebras without invoking any idea of “a reading error” or “a measured range.” Then the state preparation process in quantum measurement theory is shown to give the normal (or locally normal) states on the observable algebra. Some remarks are made concerning the physical implications of normal states for systems with an infinite number of degrees of freedom, (...) including questions on open and closed algebraic theories. (shrink)

The measurement of one or more observables can be considered to yield sample points which are in general fuzzy sets. Operationally these fuzzy sample points are the outcomes of calibration procedures undertaken to ensure the internal consistency of a scheme of measurement. By introducing generalized probability measures on σ-semifields of fuzzy events, one can view a quantum mechanical state as an ensemble of probability measures which specify the likelihood of occurrence of any specific fuzzy sample point at some instant. These (...) sample points are the possible outcomes of any infinitely rapid succession of measurements at that instant of any sequence of observables of the system. (shrink)

The purpose of the simultaneous measurement of noncommuting quantum observables can be viewed as the joint estimation of parameters of the density operator of the quantum system. Joint estimation involves the application of a multiply parameterized operator-valued measure. An example related to the simultaneous estimation of the position and velocity of a particle is given. Conceptual difficulties attending simultaneous measurement of noncommuting observables are avoided by this formation.

The ability of predicting upcoming events or conditions in advance offers substantial selective advantage to living beings. The most successful systematic tool for fairly reliable prognoses is the use of dynamical causal models in combination with memorised experience. Surprisingly, causality is a fundamental but rather controversially disputed concept. For both models and memory, symbol processing is requisite. Symbols are a necessary and sufficient attribute of life from its very beginning; the process of their evolutionary emergence was discovered by Julian Huxley (...) a century ago. In behavioural biology, this universal symmetry-breaking kinetic phase transition became known as ritualisation. Symbol use for predicting future dynamical processes has culminated in the unprecedented complexity of mental models used in science and technology, coining the historical ascent of modern humans. Observation and measurement transform structural information of physical exchange processes into symbolic information from which state quantities are derived by means of mental models. However, phylogenetically inherited models such as naïve realism do not necessarily explain the sophisticated insights revealed by modern experiments with, say, entangled quantum states. It is suggested to carefully distinguish observed exchange quantities from predicted unobservable state quantities, and physical reality from mental models thereof. (shrink)