POVM Quantization

Abstract

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 points of the measure space. We specially focus on various probabilistic aspects of these constructions. Simple or more elaborate examples illustrate the procedure: circle, 2-sphere, plane, half-plane. Links with POVM quantum measurement and quantum statistical inference are sketched.

References in corpus (4)

• Coherent States and Bayesian Duality
• Group invariant inferred distributions via noncommutative probability
• On Quantum Statistical Inference, I
• A Note on Distribution Spaces on Manifolds

Cited by in corpus (9)

• Covariant Affine Integral Quantization(s)
• From classical to quantum Oppenheimer-Snyder model: non-marginal case
• Quantum Mixmaster as a model of the Primordial Universe
• $\mathcal{D}$-Pseudo-Bosons, Complex Hermite Polynomials, and Integral Quantization
• Generalized Susskind-Glogower coherent states
• 2-D Covariant Affine Integral Quantization(s)
• Schrödinger model and Stratonovich-Weyl correspondence for Heisenberg motion groups
• Quantum formalism on the plane: POVM-Toeplitz quantization, Naimark theorem and linear polarisation of the light
• Quantum models a la Gabor for space-time metric