Related papers: Thoughts on Holographic Complexity and its Basis-d…
We obtain a general concept of triplet of Hilbert spaces with closed (unbounded) embeddings instead of continuous (bounded) ones. The construction starts with a positive selfadjoint operator $H$, that is called the Hamiltonian of the…
This Chapter develops a realist information-theoretic interpretation of the nonclassical features of quantum probabilities. On this view, what is fundamental in the transition from classical to quantum physics is the recognition that…
In quantum chemistry, the price paid by all known efficient model chemistries is either the truncation of the Hilbert space or uncontrolled approximations. Theoretical computer science suggests that these restrictions are not mere…
We propose a holographic map between Einstein gravity coupled to matter in a de Sitter background and large N quantum mechanics of a system of spins. Holography maps a spin model with a finite dimensional Hilbert space defined on a version…
We introduce a measure of ''quantumness'' for any quantum state in a finite dimensional Hilbert space, based on the distance between the state and the convex set of classical states. The latter are defined as states that can be written as a…
A geometric approach to formulate the uncertainty principle between quantum observables acting on an $N$-dimensional Hilbert space is proposed. We consider the fidelity between a density operator associated with a quantum system and a…
Useful relations describing arbitrary parameters of given quantum systems can be derived from simple physical constraints imposed on the vectors in the corresponding Hilbert space. This is well known and it usually proceeds by partitioning…
A closed vacuum-dominated Friedmann universe is asymptotic to a de Sitter space with a cosmological event horizon for any observer. The holographic principle says the area of the horizon in Planck units determines the number of bits of…
We examine the holographic complexity conjectures in the context of holographic theories of FRW spacetimes. Analyzing first the complexity-action conjecture for a flat FRW universe with one component, we find that the complexity grows as…
State space structure of tripartite quantum systems is analyzed. In particular, it has been shown that the set of states separable across all the three bipartitions [say $\mathcal{B}^{int}(ABC)$] is a strict subset of the set of states…
We define the algorithmic complexity of a quantum state relative to a given precision parameter, and give upper bounds for various examples of states. We also establish a connection between the entanglement of a quantum state and its…
We explore the structure of holographic entropy relations (associated with 'information quantities' given by a linear combination of entanglement entropies of spatial sub-partitions of a CFT state with geometric bulk dual). Such entropy…
I suggest the possibility that holographic quantum gravity is, in some sense, equivalent to quantum information theory. Some radical implications would follow. First, the theory of quantum gravity should have no adjustable coupling…
Shape complexity is a hard-to-quantify quality, mainly due to its relative nature. Biased by Euclidean thinking, circles are commonly considered as the simplest. However, their constructions as digital images are only approximations to the…
The role of complex quantities in quantum theory has been puzzling physicists since the beginnings. It is thus natural to ask whether, in order to describe our experiments, the mathematical structure of complex Hilbert spaces it is built on…
Quantum contextuality is a source of quantum computational power and a theoretical delimiter between classical and quantum structures. It has been substantiated by numerous experiments and prompted generation of state independent contextual…
Quantum coherence and distributed correlations among subparties are often considered as separate, although operationally linked to each other, properties of a quantum state. Here, we propose a measure able to quantify the contributions…
According to the stochastic-quantum correspondence, a quantum system can be understood as a stochastic process unfolding in an old-fashioned configuration space based on ordinary notions of probability and `indivisible' stochastic laws,…
Coherence is a fundamental notion in quantum mechanics, defined relative to a reference basis. As such, it does not necessarily reveal the locality of interactions nor takes into account the accessible operations in a composite quantum…
The concept of holography has lured philosophers of science for decades, and is becoming more and more popular on several fronts of science, e. g. in the physics of black holes. In this paper we try to understand things as if the visible…