We introduce a model of classical and quantum observation based on contextuality and dynamically evolving apparatus. Power sets of classical bits model the four classical states of elementary detectors, viz. the two normal yes/no signal states, the faulty or decommissioned state and the non-existence state. Operators over power set registers are used to describe various physical scenarios such as the construction and decommissioning of physical devices in otherwise empty laboratories, the dynamics of signal states over those detectors, the extraction of information from those states, and multiple observers. We apply our quantum formalism to the Elitzur-Vaidman bomb-tester experiment and the Hardy paradox experiment.
We introduce a model of classical and quantum observation based on contextuality and dynamically evolving apparatus. Power sets of classical bits model the four classical states of elementary detectors, viz. the two normal yes/no signal states, the faulty or decommissioned state and the non-existence state. Operators over power set registers are used to describe various physical scenarios such as the construction and decommissioning of physical devices in otherwise empty laboratories, the dynamics of signal states over those detectors, the extraction of information from those states, and multiple observers. We apply our quantum formalism to the Elitzur-Vaidman bomb-tester experiment and the Hardy paradox experiment.
We introduce a model of classical and quantum observation based on contextuality and dynamically evolving apparatus. Power sets of classical bits model the four classical states of elementary detectors, viz. the two normal yes/no signal states, the faulty or decommissioned state and the non-existence state. Operators over power-set registers are used to describe various physical scenarios such as the construction and decommissioning of physical devices in otherwise empty laboratories, the dynamics of signal states over those detectors, the extraction of information from those states and multiple observers. We apply our quantum formalism to the Elitzur–Vaidman bomb-tester experiment and the Hardy paradox experiment.
Introduction In this chapter we discuss how quantized detector network (QDN) theory can be extended to cover the creation and decommissioning of apparatus, from the perspective of observers and their laboratories. This extension will be referred to as extended QDN. It allows us to discuss bit power sets, laboratories, the universal register, contextual vacua, and the creation of quantized detector apparatus. This extended formalism is used to describe the Elitzur–Vaidman bomb-tester experiment and the Hardy paradox experiment. A central concept running through this book is that of the observer , the enigmatic “ I ” of I think therefore I am . The problem is that, despite the many triumphs of quantum mechanics (QM), the physics of the observer and observation is still not well understood. Regardless of how observers are defined and whether classical or quantum principles are involved, physicists generally believe that classical information in some form is extracted from systems under observation (SUOs) in actual physics experiments. In all branches of science, their language reflects this belief: experimentalists talk of measuring an electron's spin or the mass of a new particle, and so on. The conceptual issues in quantum mechanics such as wave–particle duality, quantum interference, and nonlocality gave the first indication that all might not be well with this perspective. We need only to look at the photon concept to appreciate some of the problems with the idea that photons are particles (Paul, 2004). There are experiments where a photon (that is, a signal) is detected from a crystal, but the atom “from whence it came” cannot be identified, suggesting that a cooperative process is involved, rather like the phonon concept in the physics of crystals. The problem we have with the photon-as-particle concept is the gap in logic. If the particle interpretation is taken literally, then obvious questions about the physical structure or its equivalent of such particles spring up. Does such a particle have a “surface”? If it has a surface, what is that surface made of? These and other simple (minded) questions quickly lead to the conclusion that the particle concept is a convenient and economical objectification of context. In other words, a useful illusion.
Quantum experiments are described in terms of time-dependent networks of quantum bits, each qubit representing an elementary information gateway. The emphasis is on the signal properties of apparatus rather than on systems under observation (SUOs), with the quantum states of the theory (the labstates) representing the observer's information about the state of their apparatus, rather than of any SUO. The formalism gives an efficient quantum register description related to the formalism of quantum computation. Experiments conventionally described by the PVM and POVM formalisms are treated in identical terms, the formalism providing an efficient modular approach to quantum optics experiments of arbitrary complexity.
Quantum contextuality is a fundamental nonclassical property of quantum systems, regarded as a key resource that demonstrates the computational and informational advantages of quantum over classical systems. Our present work aims to construct Hardy's paradoxes, a set of possibilistic conditions witnessing contextuality, for Yu-Oh set, which is the state-independent contextual quantum system with the least number of vectors. To achieve the aim, we systematically enumerate all logically contextual pure states on Yu-Oh set, and theoretically prove that no mixed states in this scenario are logically contextual. Based on the identified logically contextual quantum states, we construct 12 Hardy's paradoxes with identical success probability SP=11.1%. Furthermore, we present corresponding observables to experimentally witness these Hardy's paradoxes.
Introduction In this chapter we move beyond the classical register scenario discussed in the previous chapter, extending the discussion to experiments described by timedependent quantum registers of varying rank. We apply our previous discussion of the signal basis representation (SBR), the computational basis representation (CBR), signal operators, signal classes, and the CBR of signal operators to the quantum case. Our discussion of dynamics covers persistence, that is, the stability of apparatus, observers, and laboratory time, and the Born probability rule. We state the principles of quantized detector network (QDN) dynamics and show how they apply to the description of quantum experiments. We discuss the signal theorem and path summations. Persistence Our first step is to clarify what QDN assumes about the evolution of apparatus in time, because this affects the modeling. QDN is designed to reflect the behavior of apparatus in the real world and so it is not assumed in general that a given observer's apparatus is constant in time, even during a given run of an experiment. Although many experiments appear to be carried out with apparatus that persists over any given run of the experiment, and indeed, perhaps over all the runs of that experiment, that is just an incidental factor that reflects no more than an economy in construction. In practice it is invariably easier and more economical to use the same equipment over and over again rather than use it once, throw it away after each run, and build a new version ready for the next run. Lest this be thought of as a trivial point, it is nevertheless an integral and costly feature of many experiments, involving maintenance and upgrading. Indeed, in laboratories such as the Large Hadron Collider, actual run time is a small fraction of total project time. A related, significant issue has to do with the concept of ensemble , discussed in the Appendix. Persistence has everything to do with time scale , specifically, the relative laboratory time over which any piece of equipment can be meaningfully discussed as such. The degree of persistence of apparatus is as contextual as anything else in physics. If a run is relatively brief, say, over in very small fractions of a second, as in high-energy particle scattering experiments, then in such an experiment, the apparatus will behave as if it persists forever.