[12] Notably, a small set of physically motivated axioms is enough to single out the GPT representation of quantum theory. [31] Any such map is termed a process matrix. Taken at face value, quantum theory challenges many of the key tenets of the mechanical conception of reality. Matters of foundational as well as mathematical interest that are covered in detail include symmetry (and its "spontaneous" breaking), the measurement problem, the Kochen-Specker, Free Will, and Bell Theorems, the Kadison-Singer conjecture, quantization, indistinguishable particles, the quantum theory of large systems, and quantum logic, the latter in connection with the topos approach to quantum theory. In fact, there exist instances of theoretical non-quantum correlations which, a priori, do not seem physically implausible. [27] In other words: all such reconstructions are partial. The original definition of measurement contextuality can be extended to state preparations and even general physical transformations.[7]. Collapse models posit the existence of natural processes which periodically localize the wave-function. There exist different approaches to resolve this conceptual gap: Research in quantum foundations is structured along these roads. An active area of research in quantum foundations is therefore to find alternative formulations of quantum theory which rely on physically compelling principles. Moreover, they are all device-independent: this means that they can be falsified under the assumption that we can decide if two or more events are space-like separated. The rooms have ingoing and outgoing channels from which a quantum system periodically enters and leaves the room. The PBR theorem does not exclude such epistemic views on quantum states. For instance, in the pilot wave theory, the quantum wave function is interpreted as a field that guides the particle trajectory and evolves with it via a system of coupled differential equations. In contrast, a non-epistemic or ontic variable captures the notion of a “real” property of the system under consideration. [28] Such theories provide an explanation to the nonexistence of superpositions of macroscopic objects, at the cost of abandoning unitarity and exact energy conservation. From Bell's theorem, we know that classical and quantum physics predict different sets of allowed correlations. The starting point of this claim is the following mental experiment: two parties, Alice and Bob, enter a building and end up in separate rooms. The challenge posed by quantum theory is, at the minimum, to develop an intuition for the reality that it describes which is sufficient to be able to discover, explore, and harness the phenomena it encompasses. Mathematical Foundations of Quantum Theory is a collection of papers presented at the 1977 conference on the Mathematical Foundations of Quantum Theory, held in New Orleans. The formalism of process matrices starts from the observation that, given the structure of quantum states, the set of feasible quantum operations follows from positivity considerations. While those systems are in the lab, Alice and Bob are able to interact with them in any way; in particular, they can measure some of their properties. Third, one can search for a full correspondence between the mathematical elements of the quantum framework and physical phenomena: any such correspondence is called an. Fourth, one can renounce quantum theory altogether and propose a different model of the world. Harvard University Press. Much of the modern technology that fuels our lives is underpinned by quantum theory. As shown by Oreshkov et al.,[31] some process matrices describe situations where the notion of global causality breaks. Cambridge University Press. [8] Under some physical assumptions, the Pusey–Barrett–Rudolph (PBR) theorem demonstrates the inconsistency of quantum states as epistemic states, in the sense above. [1][2] Whether this should be regarded as proving that the physical world itself is "nonlocal" is a topic of debate,[3][4] but the terminology of "quantum nonlocality" is commonplace. In view of this trend, it is reasonable to postulate that any high-order map from quantum instruments (namely, measurement processes) to probabilities should also be physically realizable. And, at best, to develop a conception of physical reality which takes quantum theory fully into account, to develop a conception which is as coherent and compelling as the mechanical conception of reality, and which is capable of guiding the further development of physics. A situation is contextual when the value of an observable depends on the context in which it is measured (namely, on which other observables are being measured as well). Yet more quantum technology, such as quantum computers and quantum cryptography, is waiting in the wings, promising to transform our lives still further. Traditional Academic Publishers. Most interpretations of quantum theory stem from the desire to solve the quantum measurement problem. 1400 Washington Avenue Main: (518) 442-3300, Corporate, Nonprofit and Public-Sector Partners. This page was last edited on 10 July 2020, at 17:54. [16][17] around the same time is also based on the, The use of purification to characterize quantum theory has been criticized on the grounds that it also applies in the Spekkens toy model.[18]. The Foundations of Quantum Field Theory. [14] The work of Dakic and Brukner eliminated this “axiom of simplicity” and provided a reconstruction of quantum theory based on three physical principles. The Foundations of Quantum Theory discusses the correspondence between the classical and quantum theories through the Poisson bracket-commutator analogy. There is an on-going debate on whether the wave-function represents the epistemic state of a yet to be discovered ontic variable or, on the contrary, it is a fundamental entity. The book is organized into three parts encompassing 12 chapters that cover topics on one-and many-particle systems and relativistic quantum mechanics and field theory. Professors Caticha, Earle, Goyal, and Knuth. In Sorkin's quantum measure theory (QMT), physical systems are not modeled via unitary rays and Hermitian operators, but through a single matrix-like object, the decoherence functional. While they lead to the right experimental predictions, they do not come with a mental picture of the world where they fit. An interpretation of quantum theory is a correspondence between the elements of its mathematical formalism and physical phenomena. Scientific inquiry into the wave nature of light began in the 17th and 18th centuries, when scientists such as Robert Hooke, Christiaan Huygens and Leonhard Euler proposed a wave theory of light based on experimental observations. Taken at face value, quantum theory challenges many of the key tenets of the mechanical conception of reality. The framework of GPTs can accommodate classical and quantum physics, as well as hypothetical non-quantum physical theories which nonetheless possess quantum theory’s most remarkable features, such as entanglement or teleportation.

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