Related papers: Single-Photon Observables and Preparation Uncertai…
We report an optical detector with tunable positive operator-valued measures (POVMs). The device is based on a combination of weak-field homodyne techniques and photon-number-resolving detection. The resulting POVMs can be continuously…
In a previous paper we have presented a general scheme for the implementation of symmetric generalized measurements (POVMs) on a quantum computer. This scheme is based on representation theory of groups and methods to decompose matrices…
Vector vortex beams, featuring independent spatial modes in orthogonal polarization components, offer an increase in information density for emerging applications in both classical and quantum communication technology. Recent advances in…
We define a complete measurement of a quantum observable (POVM) as a measurement of the maximally refined version of the POVM. Complete measurements give information from the multiplicities of the measurement outcomes and can be viewed as…
Various forms of optimality for quantum observables described as normalized positive operator valued measures (POVMs) are studied in this paper. We give characterizations for observables that determine the values of the measured quantity…
In the signal-processing literature, a frame is a mechanism for performing analysis and reconstruction in a Hilbert space. By contrast, in quantum theory, a positive operator-valued measure (POVM) decomposes a Hilbert-space vector for the…
We characterize the asymptotic performance of a class of positive operator valued measurements (POVMs) where the only task is to make measurements on independent and identically distributed quantum states on finite-dimensional systems. The…
Motivated by an intention to apply partial wave analysis to systems containing photons, we construct eigenvectors of the distance of separation between two photons. A choice is made that makes the case of two photons most closely resemble…
The positive operator (valued) measures (POMs) allow one to generalize the notion of observable beyond the traditional one based on projection valued measures (PVMs). Here, we argue that this generalized conception of observable enables a…
In biorthogonal quantum mechanics, the eigenvectors of a quasi-Hermitian operator and those of its adjoint are biorthogonal and complete and the probability for a transition from a quantum state to any one of these eigenvectors is positive…
We tackle the dynamical description of the quantum measurement process, by explicitly addressing the interaction between the system under investigation with the measurement apparatus, the latter ultimately considered as macroscopic quantum…
We address the implementation of the positive operator-valued measure (POVM) describing the optimal M-outcomes discrimination of the polarization state of a single photon. Initially, the POVM elements are extended to projective operators by…
A first quantized free photon is a complex massless vector field $A=(A^\mu)$ whose field strength satisfies Maxwell's equations in vacuum. We construct the Hilbert space $\mathscr{H}$ of the photon by endowing the vector space of the fields…
We identify momentum/helicity probability amplitudes for the photon and find their relativistic transformation properties. We also find their behaviour under space inversion and time reversal. The discussion begins with a review of the…
Generalized quantum measurements (also known as POVMs) are of great importance in quantum information and quantum foundations, but often difficult to perform. We present an experimental approach which can in principle be used to perform…
The process of cavity mode quantum state photodetection subject to a nonideal measurement device is under consideration. A set of nonorthogonal probabilistic operator valued measures (POVMs) describing the photodetection process is…
We present a general formalism for giving a measure space paired with a separable Hilbert space a quantum version based on normalized positive operator-valued measure. The latter are built from families of density operators labelled by…
We study the existence of jointly measurable POVM approximations to two non-commuting sharp spin observables. We compare two different ways to specify optimal approximations.
A Positive Operator Valued Measure (POVM) is a map $F:\mathcal{B}(X)\to\mathcal{L}_s^+(\mathcal{H})$ from the Borel $\sigma$-algebra of a topological space $X$ to the space of positive self-adjoint operators on a Hilbert space…
We report an experimental implementation of a single-qubit generalised measurement scenario(POVM) based on a quantum walk model. The qubit is encoded in a single-photon polarisation. The photon performs a quantum walk on an array of optical…