On the reality of the quantum state once again (original) (raw)

Cognition according to Quantum information: Three Epistemological Puzzles Solved

2020

The cognition of quantum processes raises a series of questions about ordering and information connecting the states of one and the same system before and after measurement: Quantum measurement, quantum invariance and the nonlocality of quantum information are considered in the paper from an epistemological viewpoint. The adequate generalization of ‘measurement’ is discussed to involve the discrepancy, due to the fundamental Planck constant, between any quantum coherent state and its statistical representation as a statistical ensemble after measurement. Quantum invariance designates the relation of any quantum coherent state to the corresponding statistical ensemble of measured results. A set-theory corollary is the curious invariance to the axiom of choice: Any coherent state excludes any well-ordering and thus excludes also the axiom of choice. However the above equivalence requires it to be equated to a well-ordered set after measurement and thus requires the axiom of choice for...

Ontology, epistemology, and quantum reality

The emergence of quantum mechanics in 1920s opened an intense discussion, which continues to these days, about its interpretation. This article aims to contribute to this discussion. First, a definition of ontic (really existing) and epistemic (pertaining to knowledge) states of a quantum system is proposed. Based on these definitions, the key concepts and postulates of quantum mechanics such as quantum state collapse, measurements and system properties, and statistical inference are discussed. An alternative interpretation of degenerate ontic states is presented. The proposed ontological and epistemological framework for quantum mechanics is applied to derive some key properties of quantum probability calculus, to explain Schrödinger's cat paradox, to redefine quantum entanglement, to examine Einstein-Podolsky-Rosen (EPR) paradox, and to substantiate the principle of local causality. This framework is further compared with the quantum histories approach, quantum information approach, and spontaneous collapse approach.

An Epistemic model of Quantum State with Ontic Probability Amplitude

We first prove that the class of ontological models of the quantum state which are capable of reproducing the Born probability rule is inconsistent with the Schrodinger time evolution. Ontological models with epistemic states fall in this class. We then model the ontic state space as a complex projective Hilbert space and define a minimalist epistemic state as an average over a set of "hidden states". We show that an epistemic interpretation of quantum states is possible in such a model that allows probability amplitudes. Finally, we prove a second theorem to show that such a model is compatible with locality but ontic models are not.

On the reality of the quantum state once again: A no-go theorem for ψ-ontic models

2024

In this paper we show that ψ-ontic models, as defined by Harrigan and Spekkens (HS), cannot reproduce quantum theory. Instead of focusing on probability, we use information theoretic considerations to show that all pure states of ψ-ontic models must be orthogonal to each other, in clear violation of quantum mechanics. Given that (i) Pusey, Barrett and Rudolph (PBR) previously showed that ψ-epistemic models, as defined by HS, also contradict quantum mechanics, and (ii) the HS categorization is exhausted by these two types of models, we conclude that the HS categorization itself is problematic as it leaves no space for models that can reproduce quantum theory.

Epistemological and ontological aspects of quantum theory

arXiv (Cornell University), 2021

In this paper, epistemology and ontology of quantum states are discussed based on a completely new way of founding quantum theory. The fundamental notions are conceptual variables in the mind of an observer or in the joint minds of a group of observers. These conceptual variables are very often accessible, that is, it is possible to find values of the variables by doing experiments or by making measurements. An important notion is that of maximal accessibility. It is shown here that this new machinery may facilitate the discussion of when a specific quantum state can be given an ontological interpretation, and also the more speculative question whether all states can be given such an interpretation. The discussion here is general, and has implications for the basic problem of how one should look upon information from experiments and measurement, in particularly the question concerning when this information may reflect properties of the real world.

Quantum Mechanics: Ontology and Information

Quantum theory shows that natural laws cannot be understood as ruling single events since the latter occur randomly. Nevertheless, the physical world shows everywhere order whose source cannot be represented by the latter. It is shown that this order is due to the presence of quantum correlations. Since their e↵ect is to reduce the space of the possible events, they can be considered as causal factors. However, being correlations, they do not display the dynamic character that would be required in order to produce a determinate e↵ect. This is why they need additional local factors in order to concur to the production of a certain event. If not so, this would even imply a violation of Einstein’s locality since correlations could be used by themselves to transmit superluminal signals. Due to such a character of correlation, they can be understood as kind of potential reality needing actual (and local) context to be e↵ective. This allows also a distinction that is classically unknown between locality and globality. Such a distinction solves the important problem of measurement showing that ultimately we have irreversible local processes while globally everything is still reversible. In particular, it is a shift of information that can explain this local phenomenon. In fact, quantum systems are essentially information and also the measurement process is ultimately a dealing with information: information processing (preparing a system), information sharing (coupling a system with an apparatus) and information selection (detecting). State, observable and property appear as equivalence classes of these three procedures, respectively. Finally, the distinction between interpreted and uninterpreted ontology is considered in a Kantian perspective, but it is also shown that the approach supported here is rather a critical realism.

On the epistemic view of quantum states

Journal of Mathematical Physics, 2008

We investigate the strengths and limitations of the Spekkens toy model, which is a local hidden variable model that replicates many important properties of quantum dynamics. First, we present a set of five axioms that fully encapsulate Spekkens' toy model. We then test whether these axioms can be extended to capture more quantum phenomena, by allowing operations on epistemic as well as ontic states. We discover that the resulting group of operations is isomorphic to the projective extended Clifford Group for two qubits. This larger group of operations results in a physically unreasonable model; consequently, we claim that a relaxed definition of valid operations in Spekkens' toy model cannot produce an equivalence with the Clifford Group for two qubits. However, the new operations do serve as tests for correlation in a two toy bit model, analogous to the well known Horodecki criterion for the separability of quantum states.

Evidence for the epistemic view of quantum states: A toy theory

Physical Review A, 2007

We present a toy theory that is based on a simple principle: the number of questions about the physical state of a system that are answered must always be equal to the number that are unanswered in a state of maximal knowledge. A wide variety of quantum phenomena are found to have analogues within this toy theory. Such phenomena include: the noncommutativity of measurements, interference, the multiplicity of convex decompositions of a mixed state, the impossibility of discriminating nonorthogonal states, the impossibility of a universal state inverter, the distinction between bi-partite and tri-partite entanglement, the monogamy of pure entanglement, no cloning, no broadcasting, remote steering, teleportation, dense coding, mutually unbiased bases, and many others. The diversity and quality of these analogies is taken as evidence for the view that quantum states are states of incomplete knowledge rather than states of reality. A consideration of the phenomena that the toy theory fails to reproduce, notably, violations of Bell inequalities and the existence of a Kochen-Specker theorem, provides clues for how to proceed with this research program.

The quantum formulation derived from assumptions of epistemic processes

Journal of Physics: Conference Series, 2015

Motivated by Quantum Bayesianism I give background for a general epistemic approach to quantum mechanics, where complementarity and symmetry are the only essential features. A general definition of a symmetric epistemic setting is introduced, and for this setting the basic Hilbert space formalism is arrived at under certain technical assumptions. Other aspects of ordinary quantum mechanics will be developed from the same basis elsewhere.