Related papers: Tsirelson's Problem
One of the hallmarks of quantum theory is the realization that distinct measurements cannot in general be performed simultaneously, in stark contrast to classical physics. In this context the notions of coexistence and joint measurability…
The theory of product systems both of Hilbert spaces (Arveson systems) and product systems of Hilbert modules has reached a status where it seems appropriate to rest a moment and to have a look at what is known so far and what are open…
We propose the construction of equations of motion based on symmetries in quantum-mechanical systems, using Heisenberg's uncertainty principle as a minimal foundation. From canonical operators, two spaces of conjugate operators are…
We demonstrate that the task of determining an unknown quantum state can be accomplished efficiently by making a sequential measurement of two observables $\hat{A}$ and $\hat{B}$, provided that the two observables are chosen in such a way…
Does quantum theory apply at all scales, including that of observers? New light on this fundamental question has recently been shed through a resurgence of interest in the long-standing Wigner's friend paradox. This is a thought experiment…
In quantum many-body systems, complex dynamics delocalize the physical degrees of freedom. This spreading of information throughout the system has been extensively studied in relation to quantum thermalization, scrambling, and chaos.…
Quantum measurement and quantum operation theory is developed here by taking the relational properties among quantum systems, instead of the independent properties of a quantum system, as the most fundamental elements. By studying how the…
The possibility of defining sesquilinear forms starting from one or two sequences of elements of a Hilbert space is investigated. One can associate operators to these forms and in particular look for conditions to apply representation…
Quantum simulators hold enormous promise for advancing the modelling of materials and understanding emergent physics, such as high temperature superconductivity and topological order. While correlation functions are, typically,…
We extend Gleason's theorem to the two-dimensional Hilbert space of a qubit by invoking the standard axiom that describes composite quantum systems. The tensor-product structure allows us to derive density matrices and Born's rule for $d=2$…
In recent decades it was established that the quantum measurements of physical quantities in space-time points divided by space-like intervals may be correlated. Though such correlation follows from the formulas of quantum mechanics its…
Measurements play a crucial role in doing physics: Their results provide the basis on which we adopt or reject physical theories. In this note, we examine the effect of subjecting measurements themselves to our experience. We require that…
Quantum gravity in a closed universe faces two a priori distinct yet seemingly related issues: the problem of time and the fact that its Hilbert space dimension is one. Both have been argued to be resolvable by formulating physics relative…
It often goes unnoticed that, even for a finite number of degrees of freedom, the canonical commutation relations have many inequivalent irreducible unitary representations; the free particle and a particle in a box provide examples that…
Quantum metrology studies the use of entanglement and other quantum resources to improve precision measurement. An interferometer using N independent particles to measure a parameter X can achieve at best the "standard quantum limit" (SQL)…
An arbitrary linear relation (multivalued operator) acting from one Hilbert space to another Hilbert space is shown to be the sum of a closable operator and a singular relation whose closure is the Cartesian product of closed subspaces.…
A limitation on simultaneous measurement of two arbitrary positive operator valued measures is discussed. In general, simultaneous measurement of two noncommutative observables is only approximately possible. Following Werner's formulation,…
We develop a general framework for self-testing, in which bipartite correlations are described by states on the commuting tensor product of a pair of operator systems. We propose a definition of a local isometry between bipartite quantum…
We explore further the suggestion to describe a pre- and post-selected system by a two-state, which is determined by two conditions. Starting with a formal definition of a two-state Hilbert space and basic operations, we systematically…
Frames formed by orbits of vectors through the iteration of a bounded operator have recently attracted considerable attention, in particular due to its applications to dynamical sampling. In this article, we consider two commuting bounded…