Quantum theory from rules on information acquisition

We provide an accessible and mostly self-contained summary of a recent reconstruction of quantum theory, for qubit systems, from rules constraining an observer's acquisition of information [arXiv:1412.8323, arXiv:1511.01130]. The focus lies on the main ideas and results, not the technical details. This reconstruction offers an instructive, informational explanation for the architecture of the theory and, as a by-product, unravels new `conserved informational charges', indeed appearing in quantum theory, that characterize the unitary group and the set of pure states

Quantum theory from rules on information acquisition

We summarise a recent reconstruction of the quantum theory of qubits from rules constraining an observer's acquisition of information. This review of [arXiv:1412.8323, arXiv:1511.01130] is accessible and fairly self-contained, focussing on the main ideas and results and not the technical details. The reconstruction offers an informational explanation for the architecture of the theory and specifically for its correlation structure. In particular, it illuminates the origin of entanglement and monogamy. As a by-product, it also unravels new `conserved informational charges' from complementarity relations that characterise the unitary group and the set of pure states

Quantum theory from rules on information acquisition

We summarise a recent reconstruction of the quantum theory of qubits from rules constraining an observer's acquisition of information. This review of [arXiv:1412.8323, arXiv:1511.01130] is accessible and fairly self-contained, focussing on the main ideas and results and not the technical details. The reconstruction offers an informational explanation for the architecture of the theory and specifically for its correlation structure. In particular, it illuminates the origin of entanglement and monogamy. As a by-product, it also unravels new `conserved informational charges' from complementarity relations that characterise the unitary group and the set of pure states

Quantum theory from rules on information acquisition

We provide an accessible and mostly self-contained summary of a recent reconstruction of quantum theory, for qubit systems, from rules constraining an observer's acquisition of information [arXiv:1412.8323, arXiv:1511.01130]. The focus lies on the main ideas and results, not the technical details. This reconstruction offers an instructive, informational explanation for the architecture of the theory and, as a by-product, unravels new `conserved informational charges', indeed appearing in quantum theory, that characterize the unitary group and the set of pure states

Toolbox for reconstructing quantum theory from rules on information acquisition

We develop an operational approach for reconstructing the quantum theory of qubit systems from elementary rules on information acquisition. The focus lies on an observer O interrogating a system S with binary questions and S's state is taken as O's `catalogue of knowledge' about S. The mathematical tools of the framework are simple and we attempt to highlight all underlying assumptions. Four rules are imposed, asserting (1) a limit on the amount of information available to O; (2) the mere existence of complementary information; (3) O's total amount of information to be preserved in-between interrogations; and, (4) O's `catalogue of knowledge' to change continuously in time in-between interrogations and every consistent such evolution to be possible. This approach permits a constructive derivation of quantum theory, elucidating how the ensuing independence, complementarity and compatibility structure of O's questions matches that of projective measurements in quantum theory, how entanglement and monogamy of entanglement, non-locality and, more generally, how the correlation structure of arbitrarily many qubits and rebits arises. The rules yield a reversible time evolution and a quadratic measure, quantifying O's information about S. Finally, it is shown that the four rules admit two solutions for the simplest case of a single elementary system: the Bloch ball and disc as state spaces for a qubit and rebit, respectively, together with their symmetries as time evolution groups. The reconstruction for arbitrarily many qubits is completed in a companion paper (arXiv:1511.01130) where an additional rule eliminates the rebit case. This approach is inspired by (but does not rely on) the relational interpretation and yields a novel formulation of quantum theory in terms of questions.Comment: 78 pages, many figures, graphs and references. Version accepted for publication in Quantum (completed missing part in the proof of reversibility of time evolution, combined previous sections 6 and 7 to a rewritten section 6, added clarifications and minor corrections throughout -- overall improved presentation, but results unaffected by revision

Switching internal times and a new perspective on the 'wave function of the universe'

Despite its importance in general relativity, a quantum notion of general covariance has not yet been established in quantum gravity and cosmology, where, given the a priori absence of coordinates, it is necessary to replace classical frames with dynamical quantum reference systems. As such, quantum general covariance bears on the ability to consistently switch between the descriptions of the same physics relative to arbitrary choices of quantum reference system. Recently, a systematic approach for such switches has been developed (arXiv:1809.00556, 1809.05093, 1810.04153). It links the descriptions relative to different choices of quantum reference system, identified as the correspondingly reduced quantum theories, via the reference-system-neutral Dirac quantization, in analogy to coordinate changes on a manifold. In this work, we apply this method to a simple cosmological model to demonstrate how to consistently switch between different internal time choices in quantum cosmology. We substantiate the argument that the conjunction of Dirac and reduced quantized versions of the theory defines a complete relational quantum theory that not only admits a quantum general covariance, but, we argue, also suggests a new perspective on the 'wave function of the universe'. It assumes the role of a perspective-neutral global state, without immediate physical interpretation, that, however, encodes all the descriptions of the universe relative to all possible choices of reference system at once and constitutes the crucial link between these internal perspectives. While, for simplicity, we use the Wheeler-DeWitt formulation, the method and arguments might be also adaptable to loop quantum cosmology.Comment: 14+7 pages. Invited contribution to the special issue "Progress in Group Field Theory and Related Quantum Gravity Formalisms", Eds. S. Carrozza, S. Gielen and D. Oriti. Minor clarifications, updated references, matches published versio