Related papers: Quantum Mereology: Factorizing Hilbert Space into …

Decoherence and einselection have been effective in explaining several features of an emergent classical world from an underlying quantum theory. However, the theory assumes a particular factorization of the global Hilbert space into…

Any Hilbert space with composite dimension can be factorized into a tensor product of smaller Hilbert spaces. This allows to decompose a quantum system into subsystems. We propose a simple tractable model for a constructive study of…

The Schmidt decomposition is the go-to tool for measuring bipartite entanglement of pure quantum states. Similarly, it is possible to study the entangling features of a quantum operation using its operator-Schmidt, or tensor product…

This work outlines a consistent method of identifying subsystems in finite-dimensional Hilbert spaces, independent of the underlying inner-product structure. Such Hilbert spaces arise in $\mathcal{P}\mathcal{T}$-symmetric quantum mechanics,…

For a bi-partite quantum system defined in a finite dimensional Hilbert space we investigate in what sense entanglement change and interactions imply each other. For this purpose we introduce an entanglement operator, which is then shown to…

We discuss the question of entanglement versus separability of pure quantum states in direct product Hilbert spaces and the relevance of this issue to physics. Different types of separability may be possible, depending on the particular…

Decompositional theories describe the ways in which a global physical system can be split into subsystems, facilitating the study of how different possible partitions of a same system interplay, e.g. in terms of inclusions or signalling. In…

The minimal ingredients to describe a quantum system are a Hamiltonian, an initial state, and a preferred tensor product structure that encodes a decomposition into subsystems. We explore a top-down approach in which the subsystems emerge…

By taking the need for quantum reference frames into account, it is shown that Hilbert-space factorization is a dissipative process requiring on the order of kT to reduce by one bit an observer's uncertainty in the provenance of a…

There has been recent interest in identifying entanglement as the fundamental concept from which space may emerge. We note that the particular way that a Hilbert space is decomposed into tensor factors is important in what the resulting…

The dynamical properties of a quantum system can be profoundly influenced by its environment. Usually, the environment provokes decoherence and its action on the system can often be schematized by adding a noise term in the Hamiltonian.…

Achieving chemical accuracy for strongly correlated molecules is a defining milestone for first-generation, fault-tolerant quantum computers, yet the factorial growth of three, four, and six-index tensor contractions in coupled-cluster…

The definition of a quantum system requires a Hilbert space, a way to define the dynamics, and an algebra of observables. The structure of the observable algebra is related to a tensor product decomposition of the Hilbert space and…

We examine how to construct a spatial manifold and its geometry from the entanglement structure of an abstract quantum state in Hilbert space. Given a decomposition of Hilbert space $\mathcal{H}$ into a tensor product of factors, we…

The holographic principle and the thermodynamics of de Sitter space suggest that the total number of fundamental degrees of freedom associated with any finite-volume region of space may be finite. The naive picture of a short distance…

We present a systematic study of quantum system compression for the evolution of generic many-body problems. The necessary numerical simulations of such systems are seriously hindered by the exponential growth of the Hilbert space dimension…

In the study of open quantum systems modeled by a unitary evolution of a bipartite Hilbert space, we address the question of which parts of the environment can be said to have a "classical action" on the system, in the sense of acting as a…

We consider quantum decay and photofragmentation processes in open chaotic systems in the semiclassical limit. We devise a semiclassical approach which allows us to consistently calculate quantum corrections to the classical decay to high…

A quantum state's entanglement across a bipartite cut can be quantified with entanglement entropy or, more generally, Schmidt norms. Using only Schmidt decompositions, we present a simple iterative algorithm to maximize Schmidt norms.…

The co-emergence of locality between the Hamiltonian and initial state of the universe is studied in a simple toy model. We hypothesize a fundamental loss functional for the combined Hamiltonian and quantum state and minimize it by gradient…