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Register a new userReality, Causality, and Quantum Theory
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Authors
John-Mark A. Allen
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Quantum theory describes our universe incredibly successfully. To our classically-inclined brains, however, it is a bizarre description that requires a re-imagining of what fundamental reality, or ontology, could look like. This thesis examines different ontological features in light of the success of quantum theory, what it requires, and what it rules out. While these investigations are primarily foundational, they also have relevance to quantum information, quantum communication, and experiments on quantum systems. [abstract shortened due to arxiv restrictions]
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Unperformed measurements have no results. Unobserved results can affect future measurements.
Quantum causality extends the conventional notion of fixed causal structure by allowing channels and operations to act in an indefinite causal order. The importance of such an indefinite causal order ranges from the foundational---e.g. towards a theory of quantum gravity---to the applied---e.g. for advantages in communication and computation. In this review, we will walk through the basic theory of indefinite causal order and focus on experiments that rely on a physically realisable indefinite causal ordered process---the quantum switch.
We describe the quantum interference of a single photon in the Mach-Zehnder interferometer using the Heisenberg picture. Our purpose is to show that the description is local just like in the case of the classical electromagnetic field, the only difference being that the electric and the magnetic fields are, in the quantum case, operators (quantum observables). We then consider a single-electron Mach-Zehnder interferometer and explain what the appropriate Heisenberg picture treatment is in this case. Interestingly, the parity superselection rule forces us to treat the electron differently to the photon. A model using only local quantum observables of different fermionic modes, such as the current operator, is nevertheless still viable to describe phase acquisition. We discuss how to extend this local analysis to coupled fermionic and bosonic fields within the same local formalism of quantum electrodynamics as formulated in the Heisenberg picture.
This is an analysis of some aspects of an old but still controversial topic, superluminal quantum tunneling. Some features of quantum tunneling described in literature, such as definition of the tunneling time and a frequency range of a signal, are discussed. The argument is presented that claim of superluminal signaling allegedly observed in frustrated internal reflection experiment was based on the wrong interpretation of the tunneling process. A thought experiment similar to that in the Tolman paradox is discussed. It shows that a new factor, attenuation, comes in the interplay between tunneled signals and macroscopic causality.
Quantum causality violates classical intuitions of cause and effect and is a unique quantum feature different from other quantum phenomena such as entanglement and quantum nonlocality. In order to avoid the detection loophole in quantum causality, we initiate the study of the detection efficiency requirement for observing quantum causality. We first show that previous classical causal inequalities require detection efficiency at least 95.97% (89.44%) to show violation with quantum (nonsignaling) correlations. Next we derive a classical causal inequality I_{222} and show that it requires lower detection efficiency to be violated, 92.39% for quantum correlations and 81.65% for nonsignaling correlations, hence substantially reducing the requirement on detection. Then we extend this causal inequality to the case of multiple measurement settings and analyze the corresponding detection efficiency. After that, we show that previous quantum causal inequalities require detection efficiency at least 94.29% to violate with nonsignaling correlations. We subsequently derive a quantum causal bound J_{222} that has a lower detection efficiency requirement of 91.02% for violation with nonsignaling correlations. Our work paves the way towards an experimental demonstration of quantum causality and shows that causal inequalities significantly differ from Bell inequalities in terms of the detection efficiency requirement.
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