Related papers: Quantum Complementarity and Operator Structures
We show how interferometry can be used to characterise certain aspects of general quantum processes, in particular, the coherence of completely positive maps. We derive a measure of coherent fidelity, maximum interference visibility and the…
In this paper we study shorted operators relative to two different subspaces, for bounded operators on infinite dimensional Hilbert spaces. We define two notions of complementability in the sense of Ando for operators, and study the…
Some typical quantization ambiguities of quantum geometry are studied within isotropic models. Since this allows explicit computations of operators and their spectra, one can investigate the effects of ambiguities in a quantitative manner.…
We present a general unified approach for finding the coherent states of polynomially deformed algebras such as the quadratic and Higgs algebras, which are relevant for various multiphoton processes in quantum optics. We give a general…
An algebraic formulation of general relativity is proposed. The formulation is applicable to quantum gravity and noncommutative space. To investigate quantum gravity we develop the canonical formalism of operator geometry, after…
We review a geometric approach to classification and examination of quantum correlations in composite systems. Since quantum information tasks are usually achieved by manipulating spin and alike systems or, in general, systems with a finite…
We review "quantum" invariants of closed oriented 3-dimensional manifolds arising from operator algebras.
We investigate the separability of arbitrary dimensional tripartite sys- tems. By introducing a new operator related to transformations on the subsystems a necessary condition for the separability of tripartite systems is presented.
Private quantum channels are the quantum analogue of the classical one-time pad. Conditional expectations and trace vectors are notions that have been part of operator algebra theory for several decades. We show that the theory of…
Complementary correlations can reveal the genuine quantum correlations present in a composite quantum system. Here we investigate the relation between complementary correlations and other aspects of genuine quantum correlations. We show…
In the present paper the algebras of functions on quantum homogeneous spaces are studied. The author introduces the algebras of kernels of intertwining integral operators and constructs quantum analogues of the Poisson and Radon transforms…
The structured operators and corresponding operator identities, which appear in inverse problems for the self-adjoint and skew-self-adjoint Dirac systems with rectangular potentials, are studied in detail. In particular, it is shown that…
We consider in general terms dynamical systems with finite-dimensional, non-simply connected configuration-spaces. The fundamental group is assumed to be finite. We analyze in full detail those ambiguities in the quantization procedure that…
Quantum relations in the sense of Weaver are $M'$-bimodules, for a von Neumann algebra $M$, these generalising actual relations on a set $X$ when $M=\ell^\infty(X)$. Similarly, relations between two sets can be generalised as bimodules over…
Quantum incompatibility, referred as the phenomenon that some quantum measurements cannot be performed simultaneously, is necessary for various quantum information processing tasks, such as nonlocality and steering. When these applications…
Various topics concerning the entanglement of composite quantum systems are considered with particular emphasis concerning the strict relations of such a problem with the one of attributing objective properties to the constituents. Most of…
Quantum measurements necessarily disturb the state of physical system. Once we perform a complete measurement, the system undergoes decoherence and loses its coherence. If there is no disturbance, the state retains all of its coherence. It…
Assuming that quantum states, including pure states, represent subjective degrees of belief rather than objective properties of systems, the question of what other elements of the quantum formalism must also be taken as subjective is…
We present a hierarchical viewpoint on the operator-algebraic formulation of quantum systems, in which $C^{*}$-algebras are responsible for the universal and intrinsic description, whereas von Neumann algebras provide the detailed account…
We construct a counter example showing, for the quadratic quantization, the identity $(\Gamma(T))^*= \Gamma(T^*)$ is not necessarily true. We characterize all operators on the one-particle algebra whose quadratic quantization are…