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We report on an intrinsic relationship between the maximum-likelihood quantum-state estimation and the representation of the signal. A quantum analogy of the transfer function determines the space where the reconstruction should be done…
We consider the problem of certification of arbitrary ensembles of pure states and projective measurements solely from the experimental statistics in the prepare-and-measure scenario assuming the upper bound on the dimension of the Hilbert…
If universal quantum interaction is really connected with the coset structure of deformations of quantum states then the curvature of projective Hilbert state space should be observable. I discuss some approach to the measurement of…
The tomographic description of a quantum state is formulated in an abstract infinite dimensional Hilbert space framework, the space of the Hilbert-Schmidt linear operators, with trace formula as scalar product. Resolutions of the unity,…
The influence of repeated projective measurements on the dynamics of the state of a quantum system is studied in dependence of the time lag $\tau$ between successive measurements. In the limit of infinitely many measurements of the…
We report the experimental preparation of optical superpositions of high orbital angular momenta(OAM). Our method is based on the use of spatial light modulator to modify the standard Laguerre-Gaussian beams to bear excessive phase helices.…
We introduce the notion of an orthocomplemented subspace of a Hilbert space H, that is, a pair of orthogonal closed subspaces of H, as a two-dimensional counterpart to the one-dimensional notion of a closed subspace of H. Orthocomplemented…
We present explicit expressions for Fock-space projection operators that correspond to realistic final states in scattering experiments. Our operators automatically sum over unobserved quanta and account for non-emission into sub-regions of…
In two recent papers by the author, a new approach was suggested for quantising space-time, or space. This involved developing a procedure for quantising a system whose configuration space--or history-theory analogue--is the set of objects,…
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…
Building on the established methods for superconducting circuit quantization, we present a new theoretical framework for approximate numerical simulation of Josephson quantum circuits. Simulations based on this framework provide access to a…
In this paper, we present a general theory of finite quantum measurements, for which we assume that the state space of the measured system is a finite dimensional Hilbert space and that the possible outcomes of a measurement is a finite set…
We present a scheme for a universal device which can be programmed by quantum states to approximate a chosen projective measurement to a given precision. Our scheme can be viewed as an extension of the swap test to the instance where one…
We characterize sets of fractional orbital angular momentum (OAM) modes of a light beam using unitary-invariant properties encoded by two-mode overlaps. Using basis-independent coherence and dimension witnesses, we experimentally certify,…
We consider quantum spin systems defined on finite sets $V$ equipped with a metric. In typical examples, $V$ is a large, but finite subset of Z^d. For finite range Hamiltonians with uniformly bounded interaction terms and a unique, gapped…
The interest in quantum-optical states confined in finite-dimensional Hilbert spaces has recently been stimulated by the progress in quantum computing, quantum-optical state preparation, and measurement techniques, in particular, by the…
Using spontaneous parametric down conversion as a source of entangled photon pairs, correlations are measured between the orbital angular momentum (OAM) in a target beam (which contains an unknown object) and that in an empty reference…
This work discusses quantum states defined in a finite-dimensional Hilbert space. In particular, after the presentation of some of them and their basic properties the work concentrates on the group of the quantum optical models that can be…
In this paper we present a complete description of a stochastic semigroup of finite-dimensional projections in Hilbert space. The geometry of such semigroups is characterized by the asymptotic behavior of the widths of compact subsets with…
An octant representation of higher-order optical modes that includes Laguerre-Gaussian and Hermite-Gaussian modes is presented. The octant picture captures the high-dimensional nature of three-state optical systems and beyond, with standard…