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. Albany, NY 12222 In addition, none of the previous axioms can be experimentally falsified unless the measurement apparatuses are assumed to be tomographically complete.  All these principles limit the set of possible correlations in non-trivial ways. Local tomography: to characterize the state of a composite system it is enough to conduct measurements at each part. As shown by Oreshkov et al., some process matrices describe situations where the notion of global causality breaks. Most interpretations of quantum theory stem from the desire to solve the quantum measurement problem. Two or more separate parties conducting measurements over a quantum state can observe correlations which cannot be explained with any local hidden variable theory. That picture of reality, which was developed by Descartes, Galileo, and Newton (amongst others), underpinned the development of physics—what is now called … 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. Axioms common to these three reconstructions are: An alternative GPT reconstruction proposed by Chiribella et al.  Notably, a small set of physically motivated axioms is enough to single out the GPT representation of quantum theory.  The work of Dakic and Brukner eliminated this “axiom of simplicity” and provided a reconstruction of quantum theory based on three physical principles. Quantum Field Theory has a problem with computed quantities being infinite. In 1803 English polymath Thomas Young described the famous double-slit experiment. 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 physical principles proposed so far include no-signalling, Non-Trivial Communication Complexity, No-Advantage for Nonlocal computation, Information Causality, Macroscopic Locality, and Local Orthogonality.  Under some physical assumptions, the Pusey–Barrett–Rudolph (PBR) theorem demonstrates the inconsistency of quantum states as epistemic states, in the sense above. Professors Caticha, Earle, Goyal, and Knuth. Generalized Probabilistic Theories (GPTs) are a general framework to describe the operational features of arbitrary physical theories.  This research program has so far provided a generalization of Bell’s theorem that allows falsifying all classical theories with a superluminal, yet finite, hidden influence. The PBR theorem does not exclude such epistemic views on quantum states. Even under the assumption of strong positivity, there exist models of QMT which generate stronger-than-quantum Bell correlations.. In contrast, a non-epistemic or ontic variable captures the notion of a “real” property of the system under consideration. It is expected, therefore, that far-from-quantum physical theories should predict correlations beyond the quantum set. 1400 Washington Avenue The rooms have ingoing and outgoing channels from which a quantum system periodically enters and leaves the room. , L. Hardy introduced the concept of GPT in 2001, in an attempt to re-derive quantum theory from basic physical principles. But, since the beginning of its existence, quantum theory has been of great interest for quite another reason. Essentially, they provide a statistical description of any experiment combining state preparations, transformations and measurements. 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. Nonlocality research efforts in quantum foundations focus on determining the exact limits that classical or quantum physics enforces on the correlations observed in a Bell experi… Two or more separate parties conducting measurements over a quantum state can observe correlations which cannot be explained with any local hidden variable theory.  Such processes are called acausal. This is an investigation of whether the infinities might arise from fields that are generated by point charges.  This was followed by the more rigorous reconstruction of Masanes and Müller.. Cambridge University Press. In some models of QMT the decoherence functional is further constrained to be positive semidefinite (strong positivity). Princeton University Press. Fourth, one can renounce quantum theory altogether and propose a different model of the world. 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.
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