Related papers: Tsirelson's Problem
We study the question of how to decompose Hilbert space into a preferred tensor-product factorization without any pre-existing structure other than a Hamiltonian operator, in particular the case of a bipartite decomposition into "system"…
Consider a scenario where $N$ separated quantum systems are measured, each with one among two possible dichotomic observables. Assume that the $N$ events corresponding to the choice and performance of the measurement in each site are…
Challenging Mermin's perspective that ``correlations have physical reality; that which they correlate does not'' we argue that correlations and correlata are not fundamentally distinct. These are dual concepts depending on the tensor…
Quantum mechanics is formulated as a geometric theory on a Hilbert manifold. Images of charts on the manifold are allowed to belong to arbitrary Hilbert spaces of functions including spaces of generalized functions. Tensor equations in this…
In this study, the properties of an oscillating system composed of a pendulum connected to a seesaw and placed on a moving platform with a certain slope are analyzed. Using complex numbers to collect the information contained in the system…
We consider the representation of operators in terms of tensor networks and their application to ground-state approximation and time evolution of systems with long-range interactions. We provide an explicit construction to represent an…
The Wigner's friend type of thought experiments manifest the conceptual challenge on how different observers can have consistent descriptions of a quantum measurement event. In this paper, we analyze the extended version of Wigner's friend…
We study the system of two localized detectors (oscillators) interacting through a massless quantum field in a vacuum state via an Unruh-DeWitt coupling. This system admits an exact solution providing a good model for addressing fundamental…
For states in infinite dimensional Hilbert spaces entanglement quantities like the entanglement of distillation can become infinite. This leads naturally to the question, whether one system in such an infinitely entangled state can serve as…
In the second part of our work on observables we have shown that quantum observables in the sense of von Neumann, i.e.bounded selfadjoint operators in some von Neumann subalgebra $R$ of $L(H)$, can be represented as bounded continuous…
A non-hermitian deformation of the one-dimensional transverse Ising model is shown to have the property of quasi-hermiticity. The transverse Ising chain is obtained from the starting non-hermitian Hamiltonian through a similarity…
We show that long standing debates on the collapse and the role of the observer in quantum mechanics can be resolved experimentally via a nondistructive continuous monitoring of a single quantum system. An example of such a system, coupled…
We study a class of quantum measurement models. A microscopic object is entangled with a macroscopic pointer such that a distinct pointer position is tied to each eigenvalue of the measured object observable. Those different pointer…
The introduction of operator states and of observables in various fields of quantum physics has raised questions about the mathematical structures of the corresponding spaces. In the framework of third quantization it had been conjectured…
We begin by defining mutually unbiased (MU) observables on a finite dimensional Hilbert space. We also consider the more general concept of parts of MU observables. The relationships between MU observables, value-complementary observables…
Taking several statistical examples, in particular one involving a choice of experiment, as points of departure, and making symmetry assumptions, the link towards quantum theory developed in Helland (2005a,b) is surveyed and clarified. The…
Correlation is the basic mechanism of every measurement model, as one never accesses the measured system directly. Instead, correlations are created, codifying information about the measurable property into the environment. Here, we address…
This paper studies multipartite observables formed from sums of local self-adjoint contractions on tensor product Hilbert spaces. The square of such a sum has a parity structure: after decomposing each local product into commutator and…
It is shown that quantum mechanics is noncontextual if quantum properties are represented by subspaces of the quantum Hilbert space (as proposed by von Neumann) rather than by hidden variables. In particular, a measurement using an…
Heisenberg's intuition was that there should be a tradeoff between measuring a particle's position with greater precision and disturbing its momentum. Recent formulations of this idea have focused on the question of how well two…