Related papers: Algebra for generalised quantum observables
The mechanism of describing quantum states by standard probability (tomographic one) instead of wave function or density matrix is elucidated. Quantum tomography is formulated in an abstract Hilbert space framework, by means of the identity…
Operating quantum sensors and quantum computers would make data in the form of quantum states available for purely quantum processing, opening new avenues for studying physical processes and certifying quantum technologies. In this…
A generic unital positive operator-valued measure (POVM), which transforms a given stationary pure state to an arbitrary statistical state with perfect decoherence, is presented. This allows one to operationally realize thermalization as a…
Quantum optics potentially offers an information channel from the Universe beyond the established ones of imaging and spectroscopy. All existing cameras and all spectrometers measure aspects of the first-order spatial and/or temporal…
Given a density operator $\hat \rho$ the optical tomography map defines a one-parameter set of probability distributions $w_{\hat \rho}(X,\phi),\ \phi \in [0,2\pi),$ on the real line allowing to reconstruct $\hat \rho $. We introduce a dual…
This thesis is mainly devoted to the study of the quantum properties of optical parametric oscillators (OPOs), which are nowadays the sources of the highest-quality quantum-correlated light, apart from fundamental tools in the…
We consider the general measurement scenario in which the ensemble average of an operator is determined via suitable data-processing of the outcomes of a quantum measurement described by a POVM. We determine the optimal processing that…
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…
The paper argues that far from challenging - or even refuting - Bohm's quantum theory, the no-hidden-variables theorems in fact support the Bohmian ontology for quantum mechanics. The reason is that (i) all measurements come down to…
Given a completely positive map, we introduce a set of algebras that we refer to as its generalized multiplicative domains. These algebras are generalizations of the traditional multiplicative domain of a completely positive map and we…
A formalism for quantum error correction based on operator algebras was introduced in [1] via consideration of the Heisenberg picture for quantum dynamics. The resulting theory allows for the correction of hybrid quantum-classical…
We develop a generalised gauge theory in which the role of gauge group is played by a coalgebra and the role of principal bundle by an algebra. The theory provides a unifying point of view which includes quantum group gauge theory,…
Continuous symmetries generated with observables of a quantum theory in the Minkowski spacetime are discussed. An example of an originated in this way algebra of observables is the algebra of observables of the canonical quantum theory,…
The physical meaning of the operators is not reducible to the intrinsic relations of the quantum system, since unitary transformations can find other operators satisfying the exact same relations. The physical meaning is determined…
A generalization of the coadjoint orbit action describes the dynamics of an observer (or instrument). We consider how this fits in with the view of observables in field theory being correlations of read-outs of instruments and show how one…
The formulation of Geometric Quantization contains several axioms and assumptions. We show that for real polarizations we can generalize the standard geometric quantization procedure by introducing an arbitrary connection on the…
Algorithmic approach is based on the assumption that any quantum evolution of many particle system can be simulated on a classical computer with the polynomial time and memory cost. Algorithms play the central role here but not the…
The modern framework of state transformers, i. e., the first Kraus representation of quantum measurement, is introduced and related both to the known textbook concepts and to measurement-interaction evolution (the second Kraus…
We describe rigorous quantum measurement theory in the Heisenberg picture by applying operator deformation techniques previously used in noncommutative quantum field theory. This enables the conventional observables (represented by…
This paper considers the relevance of the concepts of observability and computability in physical theory. Observability is related to verifiability which is essential for effective computing and as physical systems are computational systems…