Quantum mechanics is a cornerstone of our current understanding of nature and extremely successful in describing physics covering a huge range of scales. However, its interpretation remains controversial since the early days of quantum mechanics. What does a quantum state really mean? Is there any way out of the so-called quantum measurement problem? Here, we present an information-complete quantum theory (ICQT) and the trinary property of nature to beat the above problems. We assume that a quantum system’s state provides an information-complete description of the system in the trinary picture. We present a consistent formalism of quantum theory that makes the information-completeness explicitly and argue that conventional quantum mechanics is an approximation of the ICQT. We then show how our ICQT provides a coherent picture and fresh angle of some existing problems in physics. The computational content of our theory is uncovered by defining an information-complete quantum computer.
Quantum mechanics is a cornerstone of our current understanding of nature and extremely successful in describing physics covering a huge range of scales. However, its interpretation remains controversial since the early days of quantum mechanics. What does a quantum state really mean? Is there any way out of the so-called quantum measurement problem? Here, we present an information-complete quantum theory (ICQT) and the trinary property of nature to beat the above problems. We assume that a quantum system’s state provides an information-complete description of the system in the trinary picture. We present a consistent formalism of quantum theory that makes the information-completeness explicitly and argue that conventional quantum mechanics is an approximation of the ICQT. We then show how our ICQT provides a coherent picture and fresh angle of some existing problems in physics. The computational content of our theory is uncovered by defining an information-complete quantum computer.
Quantum information, which studies the representation of information by quantum mechanical systems and the type of information processing this makes possible, is a relatively new field. Its roots, however, go back to early discussions of the interpretation of the quantum mechanical formalism. In 1935 Einstein, Podolsky and Rosen suggested that there were interpretational issues with quantum mechanics, having to do with local realism. Einstein was puzzled by an apparent lack of locality in quantum mechanical descriptions of reality, and suggested that quantum mechanics was not a complete theory. This stimulated a subsequent series of theoretical and experimental investigations. In particular, John Bell realized that Einstein's proposal for a ‘completion’ of quantum mechanics by the addition of more variables – called ‘hidden’ variables – was not consistent with quantum predictions, and could not be carried out. While these interpretational issues set the stage for what followed, the modern field of quantum information arose in the 1980s stimulated by the ever decreasing size of the elements in information processing circuits. It was realized that at some point a threshold would be crossed and the devices would start to exhibit quantum mechanical behavior. It was first determined that, if they did, it would not present a problem, and, in addition, it could even be advantageous. This led to the idea of a quantum computer that stores information in quantum states, or ‘qubits’, rather than as binary digits, or ‘bits’, in a standard digital computer. The field took off when, in 1994, Peter Shor found an efficient quantum algorithm for finding the prime factors of an integer.
Despite its power as the conceptual basis for a huge range of physical phenomena in atomic and subatomic physics, quantum mechanics still suffers from a lack of clarity regarding the physical meaning of its fundamental theoretical concepts, such as those of quantum state and of quantum theoretical quantities or variables , dealt with by the known mathematical-theoretical rules. These concepts have generally been considered as not giving a direct description of physical systems, for they do not correspond to what is usually understood by `physical states' or `physical properties', notably characterized by definite numerical values such as those obtained from measurement. The situation has been tentatively expressed in terms of various `interpretations', conceived not only with regard to the physical meanings of mathematical quantities, but also in connection with philosophical statements about `physical reality'. The question of whether or not quantum theoretical quantities describe definite physical systems existing in nature has therefore generally been considered as beyond the possibilities of physics, because of the definitions that are commonly taken for `physical state' and `physical quantity'. We sketch the main ideas on this problem and propose a possible way out of the puzzle, in terms of an extension of the meaning given to the concepts of the physical state and physical quantity of a system, which would allow one, without any theoretical change in quantum mechanics, to speak consistently of real quantum systems as having definite physical properties .
Quantum mechanics, one of the most successful theories in the history of science, was created to account for physical systems not describable by classical physics. Though it is consistent with all experiments conducted thus far, many of its core concepts (amplitudes, global phases, etc.) can not be directly accessed and its interpretation is still the subject of intense debate, more than 100 years since it was introduced. So, a fundamental question is why this particular mathematical model is the one that nature chooses, if indeed it is the correct model. In the past two decades there has been a renewed effort to determine what physical or informational principles define quantum mechanics. In this paper, recent attempts at establishing reasonable physical principles are reviewed and their degree of success is tabulated. An alternative approach using joint quasi-probability distributions is shown to provide a common basis of representing most of the proposed principles. It is argued that having a common representation of the principles can provide intuition and guidance to relate current principles or advance new principles. The current state of affairs, along with some alternative views are discussed.
Since the beginning, quantum mechanics has raised major foundational and interpretative problems. Foundational research has been an important factor in the development of quantum cryptography, quantum information theory and, perhaps one day, practical quantum computers. Many believe that, in turn, quantum information theory has bearing on foundational research. This is largely related to the so-called epistemic view of quantum states, which maintains that the state vector represents information on a system and has led to the suggestion that quantum theory needs no interpretation. I will argue that this and related approaches fail to take into consideration two different explanatory functions of quantum mechanics, namely that of accounting for classically unexplainable correlations between classical phenomena and that of explaining the microscopic structure of classical objects. If interpreting quantum mechanics means answering the question, “How can the world be for quantum mechanics to be true?”, there seems to be no way around it.
Since the beginning, quantum mechanics has raised major foundational and interpretative problems. Foundational research has been an important factor in the development of quantum cryptography, quantum information theory and, perhaps one day, practical quantum computers. Many believe that, in turn, quantum information theory has bearing on foundational research. This is largely related to the so-called epistemic view of quantum states, which maintains that the state vector represents information on a system and has led to the suggestion that quantum theory needs no interpretation. I will argue that this and related approaches fail to take into consideration two different explanatory functions of quantum mechanics, namely that of accounting for classically unexplainable correlations between classical phenomena and that of explaining the microscopic structure of classical objects. If interpreting quantum mechanics means answering the question, "How can the world be for quantum mechanics to be true?", there seems to be no way around it.
Rovelli’s relational interpretation of quantum mechanics tells us that the description of a system in the formalism of quantum mechanics is not an absolute but is relative to the observer itself. The interpretation goes further and proposes a set of axioms. In standard non-relational language, one of them states that an observer can only retrieve a finite amount information from a system by means of measurement. Our contribution starts with the observation that quantum mechanics, i.e., quantum field theory (QFT) in dimension 1, radically differs from QFT in higher dimensions. In higher dimensions, boundary data (or initial data) cannot be characterized by finitely many measurements. This calls for a notion of measuring scale, which we provide. At a given measuring scale, the observer has partial information about the system. Our notion of measuring scale generalizes the one implicitly used in Wilsonian QFT. At each measuring scale, there are effective theories, which may be corrected, and if the theory turns out to be renormalizable, the mentioned corrections converge to determine a completely corrected (or renormalized) theory at the given measuring scale. The notion of a measuring scale is the cornerstone of Wilsonian QFT; this notion tells us that we are not describing a system from an absolute perspective. An effective theory at that scale describes the system with respect to the observer, which may retrieve information from the system by means of measurement in a specific way determined by our notion of measuring scale. We claim that a relational interpretation of quantum physics for spacetimes of dimensions greater than 1 is Wilsonian.