Related papers: Quantum Measurements from a Logical Point of View
Kempf et al. in Ref. [1] have formulated a Hilbert space representation of quantum mechanics with a minimal measurable length. Recently it has been revealed, in the context of doubly special relativity, that a test particles' momentum…
We show that QM can be represented as a natural projection of a classical statistical model on the phase space $\Omega= H\times H,$ where $H$ is the real Hilbert space. Statistical states are given by Gaussian measures on $\Omega$ having…
Quantum mechanics owes much of its extraordinary success to a Hilbertian program of mathematical formalization. Yet, the formalism remains poorly aligned with the practical limitations of computations in finite dimensions and under finite…
A quantum measurement is logically reversible if the premeasurement density operator of the measured system can be calculated from the postmeasurement density operator and from the outcome of the measurement. This paper analyzes why many…
In quantum mechanics, the selfadjoint Hilbert space operators play a triple role as observables, generators of the dynamical groups and statistical operators defining the mixed states. One might expect that this is typical of Hilbert space…
Hilbert space combines the properties of two fundamentally different types of mathematical spaces: vector space and metric space. While the vector-space aspects of Hilbert space, such as formation of linear combinations of state vectors,…
Despite its enormous empirical success, the formalism of quantum theory still raises fundamental questions: why is nature described in terms of complex Hilbert spaces, and what modifications of it could we reasonably expect to find in some…
Quantum coherence is one of the most basic characteristics of quantum mechanics. Here we give some methods to detect and measure quantum coherence. Firstly, we propose a coherence criterion without full quantum state tomography based on…
The original purpose of measurements is to provide us with information about a previously unknown physical property of the system observed. In the Hilbert space formalism of quantum mechanics, this physical meaning of measurement…
In this paper, we extend the standard formalism of quantum mechanics to a quantum theory for a total system including one internal measuring apparatus. The internality of the measuring apparatus implies that different decomposition of a…
We characterize the class of quantum measurements that matches the applications of quantum theory to cognition (and decision making) - quantum-like modeling. Projective measurements describe the canonical measurements of the basic…
The (consistent or decoherent) histories interpretation provides a consistent realistic ontology for quantum mechanics, based on two main ideas. First, a logic (system of reasoning) is employed which is compatible with the Hilbert-space…
In these notes, based on lectures given as part of the Les Houches summer school on Quantum Optics and Nanophotonics in August, 2013, I have tried to give a brief survey of some important approaches and modern tendencies in quantum…
In this paper we investigate the potential for persuasion linked to the quantum indeterminacy of beliefs. We first formulate the persuasion problem in the context of quantum-like beliefs. We provide an economic example of belief…
Endeavoring to formulate an exhaustive solution to the measurement problem in view of the theory of decoherence leads to a better understanding of the status of the collapse and of the emergence of classicality, thanks to a precise…
The Schrodinger equation is incomplete, inherently unable to explain the collapse of the wavefunction caused by measurement; a fundamental issue known as the quantum measurement problem. Quantum mechanics is generally constrained by the…
Until recently, a quantum instrument was defined to be a completely positive operation-valued measure from the set of states on a Hilbert space to itself. In the last few years, this definition has been generalized to such measures between…
Despite quantum theory's remarkable success, many philosophers worry that it nonetheless lacks some crucial connection between theory and experiment. One under-discussed aspect of the Quantum Measurement Problems is that it is sometimes…
An alternative approach to decoherence, named non-dynamical decoherence is developed and used to resolve the quantum measurement problem. According to decoherence, the observed system is open to a macroscopic apparatus(together with a…
A realistic measurement-free theory for the quantum physics of multiple qubits is proposed. This theory is based on a symbolic representation of a fractal state-space geometry which is invariant under the action of deterministic and locally…