Positive operator-valued measure for two-photon detection via sum-frequency generation

Positive-Operator Valued Measure (POVM) Quantization

We present a general formalism for giving a measure space paired with a separable Hilbert space a quantum version based on a normalized positive operator-valued measure. The latter are built from families of density operators labeled by points of the measure space. We especially focus on various probabilistic aspects of these constructions. Simple or more elaborate examples illustrate the proce...

Positive Operator - Valued Measurements

Broadband sum-frequency generation as an efficient two-photon detector for optical tomography.

We describe a novel non-linear detection method for optical tomography that does not rely on detection of interference fringes and is free of optical background. The method exploits temporally coherent broadband illumination such as ultrashort pulses, and a non-linear two-photon detection process such as sum-frequency generation (SFG). At the detection stage, the reference beam and the sample b...

A unified description of sum frequency generation, parametric down conversion and two-photon fluorescence.

A superoperator non-equilibrium Green's function formalism is presented for computing nonlinear optical processes involving any combination of classical and quantum optical modes. Closed correlation-function expressions based on superoperator time-ordering are derived for the combined effects of causal response and non-causal spontaneous fluctuations. Coherent three wave mixing (sum frequency g...

On positive operator-valued continuous maps

In the paper the geometric properties of the positive cone and positive part of the unit ball of the space of operator-valued continuous space are discussed. In particular we show that ext-ray C+(K,L(H)) = {R+1{k0}x⊗ x : x ∈ S(H), k0 is an isolated point of K} ext B+(C(K,L(H))) = s-ext B+(C(K,L(H))) = {f ∈ C(K,L(H) : f(K) ⊂ ext B+(L(H))}. Moreover we describe exposed, strongly exposed and denti...