One of quantum theory's salient features is its apparent indeterminism, i.e. measurement outcomes are typically probabilistic. We formally define and address whether this uncertainty is unavoidable or whether post-quantum theories can offer a predictive advantage while conforming to the Born rule on average. We present a no-go claim combining three aspects: predictive advantage, no-signalling, and reliable intersubjectivity between quantum observers. The results of the analysis lead to the conclusion that there exists a fundamental limitation on genuine predictive advantage. However, we uncover a fascinating possibility: When the assumption of reliable intersubjectivity between different observers is violated, subjective predictive advantage can, in principle, exist. This, in turn, entails an epistemic boundary between different observers of the same theory. The findings reconcile us to quantum uncertainty as an aspect of limits on Nature's predictability.
One of quantum theory's salient features is its apparent indeterminism, i.e. measurement outcomes are typically probabilistic. We formally define and address whether this uncertainty is unavoidable or whether post-quantum theories can offer a predictive advantage while conforming to the Born rule on average. We present a no-go claim combining three aspects: predictive advantage, no-signalling, and reliable intersubjectivity between quantum observers. The results of the analysis lead to the conclusion that there exists a fundamental limitation on genuine predictive advantage. However, we uncover a fascinating possibility: When the assumption of reliable intersubjectivity between different observers is violated, subjective predictive advantage can, in principle, exist. This, in turn, entails an epistemic boundary between different observers of the same theory. The findings reconcile us to quantum uncertainty as an aspect of limits on Nature's predictability.
This doctoral dissertation on the foundations of quantum theory isolates and formalizes physical knowability constraints, understood here as constraints on what any conceivable observer can know about the physical world; I henceforth call these “epistemic constraints” for terseness. Here, epistemic constraints concern the definite, intersubjectively agreeable, ordinary-language conditions under which experiments are described. The usual formulation of the quantum measurement problem, which I call the Schrodingerian measurement problem, has the structure of an anomaly: if we take quantum theory at face value, we expect no definite values, and yet we see definite values in experiments. The responses to this problem have been either to solve it or to dissolve it. These responses, which have taken the form of interpretation, modification, or reconstruction of quantum mechanics, seek either to derive (conceptually or mathematically) epistemic constraints from within quantum mechanics or suitable modifications of it, as is the case with certain interpretations and modifications, or to posit the epistemic constraint, or parts of it, as a primitive assumption with the goal of deriving quantum mechanics, as is the case in some reconstruction programs. In contrast to the Schrodingerian measurement problem, which had the structure of an anomaly, this dissertation develops the Bohrian Program, which (for lack of a better comparison) has a structure similar to the problem historically associated with Euclid’s fifth postulate. It seeks to keep epistemic constraints as primitive in an onto-epistemic sense. It then seeks new physical conclusions from the joint consideration of quantum mechanics and epistemic constraints, without seeking to derive one from the other. Among other results, this leads to a notion of the probability of instantiability of the Born Rule that specifies when to apply the Born Rule and when to apply a unitary transformation to a quantum state.
This doctoral dissertation on the foundations of quantum theory isolates and formalizes physical knowability constraints, understood here as constraints on what any conceivable observer can know about the physical world; I henceforth call these “epistemic constraints” for terseness. Here, epistemic constraints concern the definite, intersubjectively agreeable, ordinary-language conditions under which experiments are described. The usual formulation of the quantum measurement problem, which I call the Schrodingerian measurement problem, has the structure of an anomaly: if we take quantum theory at face value, we expect no definite values, and yet we see definite values in experiments. The responses to this problem have been either to solve it or to dissolve it. These responses, which have taken the form of interpretation, modification, or reconstruction of quantum mechanics, seek either to derive (conceptually or mathematically) epistemic constraints from within quantum mechanics or suitable modifications of it, as is the case with certain interpretations and modifications, or to posit the epistemic constraint, or parts of it, as a primitive assumption with the goal of deriving quantum mechanics, as is the case in some reconstruction programs. In contrast to the Schrodingerian measurement problem, which had the structure of an anomaly, this dissertation develops the Bohrian Program, which (for lack of a better comparison) has a structure similar to the problem historically associated with Euclid’s fifth postulate. It seeks to keep epistemic constraints as primitive in an onto-epistemic sense. It then seeks new physical conclusions from the joint consideration of quantum mechanics and epistemic constraints, without seeking to derive one from the other. Among other results, this leads to a notion of the probability of instantiability of the Born Rule that specifies when to apply the Born Rule and when to apply a unitary transformation to a quantum state.
This doctoral dissertation on the foundations of quantum theory isolates and then formalizes a physically relevant concept that I have called "Epistemic Constraint." Here, epistemic constraints are the definite, intersubjectively agreeable, ordinary-language conditions under which experiments are described. The usual formulation of the quantum measurement problem, which I call the Schrodingerian measurement problem, has the structure of an anomaly: if we take quantum theory at face value, we expect no definite values, and yet we see definite values in experiments. The responses to this problem have been either to solve it or to dissolve it. These responses, which have taken the form of interpretation, modification, or reconstruction of quantum mechanics, seek either to derive (conceptually or mathematically) epistemic constraints from within quantum mechanics or suitable modifications of it, as is the case with certain interpretations and modifications, or to posit the epistemic constraint, or parts of it, as a primitive assumption with the goal of deriving quantum mechanics, as is the case in some reconstruction programs. In contrast to the Schrodingerian measurement problem, which had the structure of an anomaly, this dissertation develops the Bohrian Program, which (for lack of a better comparison) has a structure similar to the problem historically associated with Euclid's fifth postulate. It seeks to keep epistemic constraints as primitive in an onto-epistemic sense. It then seeks new physical conclusions from the joint consideration of quantum mechanics and epistemic constraints, without seeking to derive one from the other. Among other results, this leads to a notion of the probability of instantiability of the Born Rule that specifies when to apply the Born Rule and when to apply a unitary transformation to a quantum state.
Uncertainty principle, one of the most iconic features of quantum mechanics, was originally viewed as a fundamental limitation. Since the inception of quantum information science, researchers began to use it to achieve quantum advantages. To better understand the origin of these advantages, an essential question is: To what extent can the uncertainty principle's signatures be simulated by a single measurement? As a single measurement clearly cannot demonstrate the uncertainty principle, such a simulation, if exists, implies the claimed advantages may either stem from other quantum features, or just be reproducible in a less resourceful way. In this work, we report a series of noise-robust no-go theorems, showing that strong enough signatures of uncertainty principle cannot be simulated by a single measurement, even when assisted by quantum pre- or post-processing. This signature is modelled by complementary instruments. We completely characterise complementary instruments by a numerically feasible measure and show that they are necessary and sufficient resources for the advantage in an operational task that aims to unambiguously send classical information.
This doctoral dissertation on the foundations of quantum theory isolates and then formalizes a physically relevant concept that I have called “Epistemic Constraint.” Here, epistemic constraints are the definite, intersubjectively agreeable, ordinary-language conditions under which experiments are described. The usual formulation of the quantum measurement problem, which I call the Schrodingerian measurement problem, has the structure of an anomaly: if we take quantum theory at face value, we expect no definite values, and yet we see definite values in experiments. The responses to this problem have been either to solve it or to dissolve it. These responses, which have taken the form of interpretation, modification, or reconstruction of quantum mechanics, seek either to derive (conceptually or mathematically) epistemic constraints from within quantum mechanics or suitable modifications of it, as is the case with certain interpretations and modifications, or to posit the epistemic constraint, or parts of it, as a primitive assumption with the goal of deriving quantum mechanics, as is the case in some reconstruction programs. In contrast to the Schrodingerian measurement problem, which had the structure of an anomaly, this dissertation develops the Bohrian Program, which (for lack of a better comparison) has a structure similar to the problem historically associated with Euclid’s fifth postulate. It seeks to keep epistemic constraints as primitive in an onto-epistemic sense. It then seeks new physical conclusions from the joint consideration of quantum mechanics and epistemic constraints, without seeking to derive one from the other. Among other results, this leads to a notion of the probability of instantiability of the Born Rule that specifies when to apply the Born Rule and when to apply a unitary transformation to a quantum state.
What theoretical structures characterise our notions of what it means for a whole physical system to be the sum of its parts? We explore various aspects of this question, with emphasise on quantum theory, from the following perspective: A physical theory constitutes the definition of a set of propositions with logical relationships between them such that probabilities can be used to judge the merits of the theory, given empirical evidence. The logical relationships between the propositions characterise our semantic notions such as individuation. We distinguish between the ontological and epistemological notions of individuation. We introduce the notion of ontological individuation within the context of ontological models. A subsystem is defined as a proposition that provides necessary and sufficient information for making useful predictions. This definition to some extent generalises the notions of separability and local causality to define systems that may not be local. It highlights the unified motivations for many assumptions in the literature, such as measurement independence, and points to hidden assumptions of causality and mutual exclusivity that occur when defining systems. An epistemic no-signalling criterion gives rise to a tensor product structure for epistemic systems in quantum theory. We utilise a symmetry emergent from this structure to derive a bound on the observability of a large class of operations, dependent on only the purity of the quantum state. In particular, we derive an upper bound on the trace distance between an untransformed state and the state transformed by any trace preserving, unital operation. Our notions of epistemic systems also relate to distinguishability. It is shown that for measurements of any two (_nite outcome) particle quantum numbers on multi-fermion states, the total uncertainty, minimised over all states, is zero. This is because despite indistinguishability characterised as a constraint on the observable algebra, the appropriate correspondence between states of distinguishable and indistinguishable particles is one where the Hilbert space of indistinguishable particles relates to particles with an extra quantum number such that effective distinguishability can emerge. This Hilbert space is larger than the one for distinguishable particles and hence can (does) contain states for which the uncertainty relations for distinguishable particles are no longer valid. We conclude by arguing that in general, epistemic systems are not necessarily distinguishable; They may be only effectively distinguishable. This would imply a theory of indistinguishable modes. Several motivations are presented and the form of the theory suggested. It is hypothesised that such a theory may provide a relativistic quantum theory, alternative to quantum field theory, that satisfies cluster decomposition.