Related papers: Finite Quantum Instruments
Definition of a quantum corridor describing monitoring a quantum observable in the framework of the phenomenological restricted-path-integral (RPI) approach is generalized for the case of a finite resolution of time. The resulting evolution…
Quantum versions of control problems are often more difficult than their classical counterparts because of the additional constraints imposed by quantum dynamics. For example, the quantum LQG and quantum H infinity optimal control problems…
Random sets are used to get a continuous partition of the cardinality of the union of many overlapping sets. The formalism uses M\"obius transforms and adapts Shapley's methodology in cooperative game theory, into the context of set theory.…
The classical Hilbert space formulation of the axioms of Quantum Mechanics appears to leave open the question whether the Hermitian operators which are associated with the observables of a finite non-relativistic quantum system are uniquely…
We establish three impossibility results regarding our knowledge of the quantum state of the universe. Suppose the universal quantum state is a typical unit vector in a high-dimensional subspace $\mathscr{H}_0$ of Hilbert space…
The temporal evolution of a quantum system can be characterized by quantum process tomography, a complex task that consumes a number of physical resources scaling exponentially with the number of subsystems. An alternative approach to the…
We develop a means of simulating the evolution and measurement of a multipartite quantum state under discrete or continuous evolution using another quantum system with states and operators lying in a real Hilbert space. This extends…
We show that in finite dimension a quantum measurement with continuous set of outcomes is always equivalent to a continuous random choice of measurements with only finite outcomes.
Symmetric informationally complete measurements are both important building blocks in many quantum information protocols and the seminal example of a generalised, non-orthogonal, quantum measurement. In higher-dimensional systems, these…
Within a simple quantization scheme, observables for a large class of finite dimensional time reparametrization invariant systems may be constructed by integration over the manifold of time labels. This procedure is shown to produce a…
We study the problem of performing orthogonal qubit measurements simultaneously. Since these measurements are incompatible, one has to accept additional imprecision. An optimal joint measurement is the one with the least possible…
We propose a general method for introducing extensive characteristics of quantum entanglement. The method relies on polynomials of nilpotent raising operators that create entangled states acting on a reference vacuum state. By introducing…
We consider iterated function systems (finite or countable), together with linear and continuous operators on Hilbert spaces, which enable us to construct Markov-type operators. Under suitable conditions, these Markov-type operators have…
Defining the observable ${\bf \phi}$ canonically conjugate to the number observable ${\bf N}$ has long been an open problem in quantum theory. Here we show how to define the absolute phase observable ${\bf \Phi}\equiv |{\bf\phi}|$ by…
Any single system whose space of states is given by a separable Hilbert space is automatically equipped with infinitely many hidden tensor-like structures. This includes all quantum mechanical systems as well as classical field theories and…
We introduce a family of operations in quantum mechanics that one can regard as "universal quantum measurements" (UQMs). These measurements are applicable to all finite-dimensional quantum systems and entail the specification of only a…
We initiate the systematic study of experimental quantum physics from the perspective of computational complexity. To this end, we define the framework of quantum algorithmic measurements (QUALMs), a hybrid of black box quantum algorithms…
Consider the polynomial ring in countably infinitely many variables over a field of characteristic zero, together with its natural action of the infinite general linear group G. We study the algebraic and homological properties of finitely…
Leveraging the techniques found in the literature on Quantum Equilibration for finite dimensional systems, we develop the theory of Quantum Equilibration for the case of infinite-dimensional systems, particularly the cases where the…
We propose a classification of measurement apparatuses based on their reliability and accessibility. Our notion of reliability parameterises the possibility of getting unexpected wrong results when using the apparatus in a given time…