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  1.  7
    Noise–Disturbance Relation and the Galois Connection of Quantum Measurements.Claudio Carmeli, Teiko Heinosaari, Takayuki Miyadera & Alessandro Toigo - 2019 - Foundations of Physics 49 (6):492-505.
    The relation between noise and disturbance is investigated within the general framework of Galois connections. Within this framework, we introduce the notion of leak of information, mathematically defined as one of the two closure maps arising from the observable-channel compatibility relation. We provide a physical interpretation for it, and we give a comparison with the analogous closure maps associated with joint measurability and simulability for quantum observables.
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  2.  29
    Symmetry, Reference Frames, and Relational Quantities in Quantum Mechanics.Leon Loveridge, Takayuki Miyadera & Paul Busch - 2018 - Foundations of Physics 48 (2):135-198.
    We propose that observables in quantum theory are properly understood as representatives of symmetry-invariant quantities relating one system to another, the latter to be called a reference system. We provide a rigorous mathematical language to introduce and study quantum reference systems, showing that the orthodox “absolute” quantities are good representatives of observable relative quantities if the reference state is suitably localised. We use this relational formalism to critique the literature on the relationship between reference frames and superselection rules, settling a (...)
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  3.  22
    Energy-Time Uncertainty Relations in Quantum Measurements.Takayuki Miyadera - 2016 - Foundations of Physics 46 (11):1522-1550.
    Quantum measurement is a physical process. A system and an apparatus interact for a certain time period, and during this interaction, information about an observable is transferred from the system to the apparatus. In this study, we quantify the energy fluctuation of the quantum apparatus required for this physical process to occur autonomously. We first examine the so-called standard model of measurement, which is free from any non-trivial energy–time uncertainty relation, to find that it needs an external system that switches (...)
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  4.  29
    Strongly Incompatible Quantum Devices.Teiko Heinosaari, Takayuki Miyadera & Daniel Reitzner - 2014 - Foundations of Physics 44 (1):34-57.
    The fact that there are quantum observables without a simultaneous measurement is one of the fundamental characteristics of quantum mechanics. In this work we expand the concept of joint measurability to all kinds of possible measurement devices, and we call this relation compatibility. Two devices are incompatible if they cannot be implemented as parts of a single measurement setup. We introduce also a more stringent notion of incompatibility, strong incompatibility. Both incompatibility and strong incompatibility are rigorously characterized and their difference (...)
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  5.  8
    Relative Quantum Time.Leon Loveridge & Takayuki Miyadera - 2019 - Foundations of Physics 49 (6):549-560.
    The need for a time-shift invariant formulation of quantum theory arises from fundamental symmetry principles as well as heuristic cosmological considerations. Such a description then leaves open the question of how to reconcile global invariance with the perception of change, locally. By introducing relative time observables, we are able to make rigorous the Page–Wootters conditional probability formalism to show how local Heisenberg evolution is compatible with global invariance.
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