Although quantum states nicely express interference effects, outcomes of experimental trials show no states directly; they indicate properties of probability distributions for outcomes. We prove categorically that probability distributions leave open a choice of quantum states and operators and particles, resolvable only by a move beyond logic, which, inspired or not, can be characterized as a guess. By recognizing guesswork as inescapable in choosing quantum states and particles, we free up the use of particles as theoretical inventions by which to describe experiments with devices, and thereby replace the postulate of state reductions by a theorem. By using the freedom to invent probe particles in modeling light detection, we develop a quantum model of the balancing of a light-induced force, with application to models and detecting devices by which to better distinguish one source of weak light from another. Finally, we uncover a symmetry between entangled states and entangled detectors, a dramatic example of how the judgment about what light state is generated by a source depends on choosing how to model the detector of that light.
Although quantum states nicely express interference effects, outcomes of experimental trials show no states directly; they indicate properties of probability distributions for outcomes. We prove categorically that probability distributions leave open a choice of quantum states and operators and particles, resolvable only by a move beyond logic, which, inspired or not, can be characterized as a guess. By recognizing guesswork as inescapable in choosing quantum states and particles, we free up the use of particles as theoretical inventions by which to describe experiments with devices, and thereby replace the postulate of state reductions by a theorem. By using the freedom to invent probe particles in modeling light detection, we develop a quantum model of the balancing of a light-induced force, with application to models and detecting devices by which to better distinguish one source of weak light from another. Finally, we uncover a symmetry between entangled states and entangled detectors, a dramatic example of how the judgment about what light state is generated by a source depends on choosing how to model the detector of that light.
Strong light signals are detected reliably on a time scale of a nanosecond; however, known detectors of weak light signals used in quantum key distribution (QKD) are much slower; they involve pulse-shaping arbiters based on flip-flops that take many nanoseconds to produce a stable output. Based on a recently shown logical independence of quantum particles from the devices that they are employed to explain, we make use of quantum mechanics fine-tuned so that particles serve not as rigid foundations but as improvised hypotheses useful in models that describe the recorded behavior of devices. On the experimental side, we augment the arbitrating flip-flop of a detector so that it fans out to a matched pair of auxiliary flip-flops, and show how this imparts to a detector a "self-awareness" of its own teetering, as announced by disagreements between the auxiliary flip-flops. We introduce a quantum model of this arrangement, invoking a pair of probe particles, and show this model corresponds well to an experiment. The matched pair of auxiliary flip-flops not only confirms the model of hesitation in a detector, but serves as an instrument, both conceptual and practical, that gives an added dimension to the characterization of signal sources.
Currently there is interest in the possibility of using quantum-mechanically entangled light to enhance the spatial resolution of sensors. Here I review some applications of equations in quantum-mechanical form to the design of sensors and related systems. In order to consider comparing equations against experiments, we will need to distinguish models comprised of mathematical formulas, whether quantum-mechanical or classical, from experiments with devices such as lasers and light detectors. The following sections sketch: * two known ways to connect quantum models to experiments (one statistical-mechanical, the other by way of probabilities); * an approximate way to translate from equations of classical electromagnetism to the quantum language of photons and detection probabilities, concentrating on interferometric effects; * quantum-mechanically suggested possibilities and obstacles for light-based radar (lidar) to enhance positional accuracy and spatial resolution; * a recently proved universal gap between, on one hand, quantum-mechanical models composed of equations and, on the other hand, experiments with devices, with the consequent need and opportunities for a designer to choose models as descriptions of measured behavior.
Introduction The use of parameters to describe an experimenter's control over the devices used in an experiment is familiar in quantum physics, for example in connection with Bell inequalities. Parameters are also interesting in a different but related context, as we noticed when we proved a formal separation in quantum mechanics between linear operators and the probabilities that these operators generate. In comparing an experiment against its description by a density operator and detection operators, one compares tallies of experimental outcomes against the probabilities generated by the operators but not directly against the operators. Recognizing that the accessibility of operators to experimental tests is only indirect, via probabilities, motivates us to ask what probabilities tell us about operators, or, put more precisely, “what combinations of a parameterized density operator and parameterized detection operators generate any given set of parametrized probabilities?” Here, we review and augment recent proofs that any given parameterized probabilities can be generated in very diverse ways, so that a parameterized probability measure, detached from any of the (infinitely many) parameterized operators that generate it, becomes an interesting object in its own right. By detaching a parameterized probability measure from the operators that may have led us to it, we (1) strengthen Holevo's bound on a quantum communication channel and (2) clarify a role for multiple levels of modeling in an example based on quantum key distribution. We then inquire into some parameterized probability measures generated by entangled states and into the topology of the associated parameter spaces; in particular we display some previously overlooked topological features of level sets of these probability measures.
The basic postulates The statistical interpretation of the wavefunction is in accord with experimental facts. An interference pattern on a screen is built up by a series of apparently random events, and the wavefunction correctly predicts where the particle is most likely to land over an ensemble of trials (cf. the frontispiece ). Yet the interpretation of the wavefunction which ascribes to it a purely statistical significance is not forced on us by the experimental results – the latter show only that it is consistent to regard the wavefunction as containing information on probability; they do not exclude the possibility that it may possess other properties. On the contrary, one may take the view that the characteristic distribution of spots on a screen which build up an interference pattern is evidence that the wavefunction indeed has a more potent physical role than a mere repository of information on probabilities, for how are the particles guided so that statistically they fall into such a pattern? Such a question is naturally ruled out by the purely probabilistic interpretation. But the latter is appropriate only if we wish to reduce physics to a kind of algorithm which is efficient at correlating the statistical results of experiments. If we wish to do more, and attempt to understand the experimental results as the outcome of a causally connected series of individual processes, then we are free to enquire as to the possible further significance of the wavefunction (beyond its probabilistic aspect), and to introduce other concepts in addition to the wavefunction.
Physics has long lived with a schizophrenia that desires determinism for measured systems while demanding that experimenters decide what to measure on a whim. Intriguingly, such a free will assumption for experimenters has thwarted many attempts to provide a satisfactory explanation of how quantum probabilities evolve to clear-cut measurements. An overview of this quantum measurement problem is presented without equations, and the lesson is drawn that denial of experimenters' free will may be the only workable solutions. If the free will assumption is rejected, then a door is open that may ultimately reconcile quantum mechanics with the definiteness of individual experiments. A holistic view is offered for an Escher-like self-consistent space-time net of events rather than a conspiracy of initial conditions as a way forward.
Although quantum states nicely explain experiments, the outcomes of experiments are not states. Instead, outcomes correspond to probability distributions. Twenty years ago we proved categorically that probability distributions leave open a choice of quantum states to explain experiments that is resolvable only by a move beyond logic, which, inspired or not, can be characterized as a guess. Guesses link the inner lives of investigators to their explanations of experimental results. Recognizing the inescapability of guesswork in physics leads to avenues of investigation, one of which is presented here. We invert the quest for the logical foundations of physics to reveal a physical basis for logic and calculation, and we represent this basis mathematically, in such a way as to show the shaping and re-shaping of calculations by guesswork. We draw on the interplay between guessing and computation in digital contexts that, perhaps surprisingly, include living organisms. Digital computation and communication depend on a type of synchronization that coordinates transitions among physically distinct conditions represented by "digits." This logical synchronization, known to engineers but neglected in physics, requires guesswork for its maintenance. By abstracting digital hardware, we model the structure of human thinking as logically synchronized computation, punctuated by guesses. We adapt marked graphs to mathematically represent computation and represent guesses by unpredictable changes in these marked graphs. The marked graphs reveal a logical substructure to spatial and temporal navigation, with implications across physics and its biological applications. By limiting our model to the logical aspect of communications and computations we unveil logical structure in relation to guesswork, applicable not just to electronics but also to the functioning of living organisms.