Related papers: Measures of distance in quantum mechanics
We show how quantum mechanics can be understood as a space-time theory provided that its spatial continuum is modelled by a variable real number (qrumber) continuum. Such a continuum can be constructed using only standard Hilbert space…
The gravity is classically formulated as the geometric curvature of the space-time in general relativity which is completely different from the other well-known physical forces. Since seeking a quantum framework for the gravity is a great…
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,…
The identification of physical subsystems in quantum mechanics as compared to classical mechanics poses significant conceptual challenges, especially in the context of quantum gravity. Traditional approaches associate quantum systems with…
In this paper, we present a general theory of finite quantum measurements, for which we assume that the state space of the measured system is a finite dimensional Hilbert space and that the possible outcomes of a measurement is a finite set…
A one-to-one correspondence is established between linearized space-time metrics of general relativity and the wave equations of quantum mechanics. Also, the key role of boundary conditions in distinguishing quantum mechanics from classical…
We study quantum statistical inference tasks of hypothesis testing and their canonical variations, in order to review relations between their corresponding figures of merit---measures of statistical distance---and demonstrate the crucial…
In Quantum Physics, a measurement is represented by a projection on some closed subspace of a Hilbert space. We study algebras of operators that abstract from the algebra of projections on closed subspaces of a Hilbert space. The properties…
An analysis of quantum measurement is presented that relies on an information-theoretic description of quantum entanglement. In a consistent quantum information theory of entanglement, entropies (uncertainties) conditional on measurement…
We overcome one of Bell's objections to `quantum measurement' by generalizing the definition to include systems outside the laboratory. According to this definition a {\sl generalized quantum measurement} takes place when the value of a…
Quantum coherence and non-classical correlation are key features of quantum world. Quantifying coherence and non-classical correlation are two key tasks in quantum information theory. First, we present a bona fide measure of quantum…
We extend the Hilbert-Schmidt (square norm) distance, previously used to define the geometric quantum discord, to define also geometric quantifiers of total and classical correlations. We then compare the dynamics of geometric and entropic…
An adapted representation of quantum mechanics sheds new light on the relationship between quantum states and classical states. In this approach the space of quantum states splits into a product of the state space of classical mechanics and…
Familiar formulations of classical and quantum mechanics are shown to follow from a general theory of mechanics based on pure states with an intrinsic probability structure. This theory is developed to the stage where theorems from quantum…
The notion of distance in Hilbert space is relevant in many scenarios. In particular, distances between quantum states play a central role in quantum information theory. An appropriate measure of distance is the quantum Jensen Shannon…
A framework for categorizing entropic measures of nonclassical correlations in bipartite quantum states is presented. The measures are based on the difference between a quantum entropic quantity and the corresponding classical quantity…
This paper is a sequel to the series of papers [gr-qc/9409010, gr-qc/9505034, gr-qc/9603022, gr-qc/9609035, gr-qc/9609046, gr-qc/9704033, gr-qc/9704038, gr-qc/9708014, gr-qc/9802016, gr-qc/9802022]. We define a quantum measurement as a…
Quantum measurement is a class of quantum channels that sends quantum states to classical states. We set up resource theories of quantum coherence and quantum entanglement for quantum measurements and find relations between them. For this,…
We propose a "guide" towards quantisation of gravity based on quantum matter in a statistical mechanics context. On one hand, a statistical mechanics model naturally arises from the thermodynamic interpretation of horizons in Rindler space.…
In a previous work [arXiv:2009.03428] we proposed a new model for Quantum GRavity(QGR) and cosmology, dubbed $SU(\infty)$-QGR. One of the axioms of this model is that Hilbert spaces of the Universe and its subsystems represent $SU(\infty)$…