Related papers: Generalized entropy for general subregions in quan…
An intriguing feature of type II$_1$ von Neumann algebra is that the entropy of the mixed states is negative. Although the type classification of von Neumann algebra and its consequence in holography have been extensively explored recently,…
The trace over the degrees of freedom located in a subset of the space transforms the vacuum state into a density matrix with non zero entropy. This geometric entropy is believed to be deeply related to the entropy of black holes. Indeed,…
Near horizons, quantum fields of low spin exhibit densities of states that behave asymptotically like 1+1 dimensional conformal field theories. In effective field theory, imposing some short-distance cutoff, one can compute thermodynamic…
Quantum physics, despite its observables being intrinsically of a probabilistic nature, does not have a quantum entropy assigned to them. We propose a quantum entropy that quantify the randomness of a pure quantum state via a conjugate pair…
This paper investigates the relationship between categorical entropy and von Neumann entropy of quantum lattices. We begin by studying the von Neumann entropy, proving that the average von Neumann entropy per site converges to the logarithm…
Quantum Field Theory (QFT) represents a vast generalization of Quantum Mechanics (QM), as it deals with systems that have an infinite number of degrees of freedom. The Stone-von Neumann theorem, which establishes the equivalence of…
The notion of {\em entanglement entropy} in quantum mechanical systems is an important quantity, which measures how much a physical state is entangled in a composite system. Mathematically, it measures how much the state vector is not…
The quantum Stein's lemma is a fundamental result of quantum hypothesis testing in the context of distinguishing two quantum states. A recent conjecture, known as the ``generalized quantum Stein's lemma", asserts that this result is true in…
We argue that the requirement of a finite entanglement entropy of quantum degrees of freedom across a boundary surface is closely related to the phenomenon of running spectral dimension, universal in approaches to quantum gravity. If…
Quantum Field Theory (QFT) introduced us to the notion that a causal diamond in space-time corresponded to a subsystem of a quantum mechanical system defined on the global space-time. Work by Jacobson\cite{ted95}, Fischler and…
For a quantum state undergoing unitary Schr\"odinger time evolution, the von Neumann entropy is constant. Yet the second law of thermodynamics, and our experience, show that entropy increases with time. Ingarden introduced the quantum…
We present a mathematical structure which unifies mathematical structures of general relativity and quantum mechanics. It consists of the noncommutative algebra of compactly supported, complex valued functions ${\mathcal A}$, with…
We study the algebra of observables in semiclassical quantum gravity for cosmological backgrounds, focusing on two key examples: slow-roll inflation and evaporating Schwarzschild-de Sitter black holes. In both cases, we demonstrate the…
If quantum gravity respects the principles of quantum mechanics, suitably generalized, it may be that a more viable approach to the theory is through identifying the relevant quantum structures rather than by quantizing classical spacetime.…
We will argue in this paper that the type classification of v.Neumann algebras play an important role in a theory of quantum gravity and quantum space-time physics. We provide arguments that type $II_{\infty}$ and its representation as a…
We consider entropy in Generalized Non-Signalling Theory (also known as box world) where the most common definition of entropy is the measurement entropy. In this setting, we completely characterize the set of allowed entropies for a…
The vacuum of quantum fields contains correlated fluctuations. When restricted to one side of a surface these have a huge entropy of entanglement that scales with the surface area. If UV physics renders this entropy finite, then a…
The entanglement entropy of a pure quantum state of a bipartite system is defined as the von Neumann entropy of the reduced density matrix obtained by tracing over one of the two parts. Critical ground states of local Hamiltonians in one…
Observational entropy provides a general notion of quantum entropy that appropriately interpolates between Boltzmann's and Gibbs' entropies, and has recently been argued to provide a useful measure of out-of-equilibrium thermodynamic…
In a series of papers we proposed a model unifying general relativity and quantum mechanics. The idea was to deduce both general relativity and quantum mechanics from a noncommutative algebra ${\cal A}_{\Gamma}$ defined on a transformation…