There is great interest in quantum mechanics as an "emergent" phenomenon. The program holds that nonobvious patterns and laws can emerge from complicated physical systems operating by more fundamental rules. We find a new approach where quantum mechanics itself should be viewed as an information management tool not derived from physics nor depending on physics. The main accomplishment of quantum-style theory comes in expanding the notion of probability. We construct a map from macroscopic information as data" to quantum probability. The map allows a hidden variable description for quantum states, and efficient use of the helpful tools of quantum mechanics in unlimited circumstances. Quantum dynamics via the time-dependent Shroedinger equation or operator methods actually represents a restricted class of classical Hamiltonian or Lagrangian dynamics, albeit with different numbers of degrees of freedom. We show that under wide circumstances such dynamics emerges from structureless dynamical systems. The uses of the quantum information management tools are illustrated by numerical experiments and practical applications
There is great interest in quantum mechanics as an "emergent" phenomenon. The program holds that nonobvious patterns and laws can emerge from complicated physical systems operating by more fundamental rules. We find a new approach where quantum mechanics itself should be viewed as an information management tool not derived from physics nor depending on physics. The main accomplishment of quantum-style theory comes in expanding the notion of probability. We construct a map from macroscopic information as data" to quantum probability. The map allows a hidden variable description for quantum states, and efficient use of the helpful tools of quantum mechanics in unlimited circumstances. Quantum dynamics via the time-dependent Shroedinger equation or operator methods actually represents a restricted class of classical Hamiltonian or Lagrangian dynamics, albeit with different numbers of degrees of freedom. We show that under wide circumstances such dynamics emerges from structureless dynamical systems. The uses of the quantum information management tools are illustrated by numerical experiments and practical applications
Quantum mechanics is basically a mathematical recipe on how to construct physical models. Historically its origin and main domain of application has been in the microscopic regime, although it strictly seen constitutes a general mathematical framework not limited to this regime. Since it is a statistical theory, the meaning and role of probabilities in it need to be defined and understood in order to gain an understanding of the predictions and validity of quantum mechanics. The interpretational problems of quantum mechanics are also connected with the interpretation of the concept of probability. In this thesis the use of probability theory as extended logic, in particular in the way it was presented by E. T. Jaynes, will be central. With this interpretation of probabilities they become a subjective notion, always dependent on one's state of knowledge or the context in which they are assigned, which has consequences on how things are to be viewed, understood and tackled in quantum mechanics. For instance, the statistical operator or density operator, is usually defined in terms of probabilities and therefore also needs to be updated when the probabilities are updated by acquisition of additional data. Furthermore, it is a context dependent notion, meaning, e.g., that two observers will in general assign different statistical operators to the same phenomenon, which is demonstrated in the papers of the thesis. It is also presented an alternative and conceptually clear approach to the problematic notion of "probabilities of probabilities", which is related to such things as probability distributions on statistical operators. In connection to this, we consider concrete numerical applications of Bayesian quantum state assignment methods to a three-level quantum system, where prior knowledge and various kinds of measurement data are encoded into a statistical operator, which can then be used for deriving probabilities of other measurements. The thesis also offers examples of an alternative quantum state assignment technique, using maximum entropy methods, which in some cases are compared with the Bayesian quantum state assignment methods. Finally, the interesting and important problem whether the statistical operator, or more generally quantum mechanics, gives a complete description of "objective physical reality" is considered. A related concern is here the possibility of finding a "local hidden-variable theory" underlying the quantum mechanical description. There have been attempts to prove that such a theory cannot be constructed, where the most well-known impossibility proof claiming to show this was given by J. S. Bell. In connection to this, the thesis presents an idea for an interpretation or alternative approach to quantum mechanics based on the concept of space-time.
Is quantum mechanics about 'states'? Or is it basically another kind of probability theory? It is argued that the elementary formalism of quantum mechanics operates as a well-justified alternative to 'classical' instantiations of a probability calculus. Its providing a general framework for prediction accounts for its distinctive traits, which one should be careful not to mistake for reflections of any strange ontology. The suggestion is also made that quantum theory unwittingly emerged, in Schroedinger's formulation, as a 'lossy' by-product of a quantum-mechanical variant of the Hamilton-Jacobi equation. As it turns out, the effectiveness of quantum theory qua predictive algorithm makes up for the computational impracticability of that master equation.
In quantum information processing it may be possible to have efficient computation and secure communication beyond the limitations of classical systems. In a fundamental point of view, however, evolution of quantum systems by the laws of quantum mechanics is more restrictive than classical systems, identified to a specific form of dynamics, that is, unitary transformations and, consequently, positive and completely positive maps to subsystems. This also characterizes classes of disallowed transformations on quantum systems, among which positive but not completely maps are of particular interest as they characterize entangled states, a general resource in quantum information processing. Structural physical approximation offers a systematic way of approximating those non-physical maps, positive but not completely positive maps, with quantum channels. Since it has been proposed as a method of detecting entangled states, it has stimulated fundamental problems on classifications of positive maps and the structure of Hermitian operators and quantum states, as well as on quantum measurement such as quantum design in quantum information theory. It has developed efficient and feasible methods of directly detecting entangled states in practice, for which proof-of-principle experimental demonstrations have also been performed with photonic qubit states. Here, we present a comprehensive review on quantum information processing with structural physical approximations and the related progress. The review mainly focuses on properties of structural physical approximations and their applications toward practical information applications.
Quantum mechanics is our most successful physical theory. However, it raises conceptual issues that have perplexed physicists and philosophers of science for decades. This 2004 book develops an approach, based on the proposal that quantum theory is not a complete, final theory, but is in fact an emergent phenomenon arising from a deeper level of dynamics. The dynamics at this deeper level are taken to be an extension of classical dynamics to non-commuting matrix variables, with cyclic permutation inside a trace used as the basic calculational tool. With plausible assumptions, quantum theory is shown to emerge as the statistical thermodynamics of this underlying theory, with the canonical commutation/anticommutation relations derived from a generalized equipartition theorem. Brownian motion corrections to this thermodynamics are argued to lead to state vector reduction and to the probabilistic interpretation of quantum theory, making contact with phenomenological proposals for stochastic modifications to Schrödinger dynamics.
I review the proposal made in my 2004 book [1], that quantum theory is an emergent theory arising from a deeper level of dynamics. The dynamics at this deeper level is taken to be an extension of classical dynamics to non-commuting matrix variables, with cyclic permutation inside a trace used as the basic calculational tool. With plausible assumptions, quantum theory is shown to emerge as the statistical thermodynamics of this underlying theory, with the canonical commutation-anticommutation relations derived from a generalized equipartition theorem. Brownian motion corrections to this thermodynamics are argued to lead to state vector reduction and to the probabilistic interpretation of quantum theory, making contact with phenomenological proposals [2, 3] for stochastic modifications to Schrödinger dynamics.
In this article, we will examine new fundamental aspects of "emergence" and "information" using novel approaches to quantum mechanics which originated from the group around Aharonov. The two-state vector formalism provides a complete description of pre- and post-selected quantum systems and has uncovered a host of new quantum phenomena which were previously hidden. The most important feature is that any weak coupling to a pre- and post-selected system is effectively a coupling to a "weak value" which is given by a simple expression depending on the two-state vector. In particular, weak values, are the outcomes of so called "weak measurements" which have recently become a very powerful tool for ultra-sensitive measurements. Using weak values, we will show how to separate a particle from its properties, not unlike the Cheshire cat story: "Well! I've often seen a cat without a grin," thought Alice; "but a grin without a cat! It's the most curious thing I ever saw in all my life!" Next, we address the question whether the physics on different scales "emerges" from quantum mechanics or whether the laws of physics at those scales are fundamental. We show that the classical limit of quantum mechanics is a far more complicated issue; it is in fact dramatically more involved and it requires a complete revision of all our intuitions. The revised intuitions can then serve as a guide to finding novel quantum effects. Next we show that novel experimental aspects of contextuality can be demonstrated with weak measurements and these suggest new restrictions on hidden variable approaches. Next we emphasize that the most important implication of the Aharonov-Bohm effect is the existence of non-local interactions which do not violate causality. Finally, we review some generalizations of quantum mechanics and their implications for "emergence" and "information." First, we review an alternative approach to quantum evolution in which each moment of time is viewed as a new "universe" and time evolution is given by correlations between different moments. Next, we present a new solution to the measurement problem involving future boundary conditions placed on the universe as a whole. Finally, we introduce another fundamental approach to quantum evolution which allows for tremendous richness in the types of allowable Hamiltonians.