Poisson Quantum Information

Abstract

By taking a Poisson limit for a sequence of rare quantum objects, I derive simple formulas for the Uhlmann fidelity, the quantum Chernoff quantity, the relative entropy, and the Helstrom information. I also present analogous formulas in classical information theory for a Poisson model. An operator called the intensity operator emerges as the central quantity in the formalism to describe Poisson states. It behaves like a density operator but is unnormalized. The formulas in terms of the intensity operators not only resemble the general formulas in terms of the density operators, but also coincide with some existing definitions of divergences between unnormalized positive-semidefinite matrices. Furthermore, I show that the effects of certain channels on Poisson states can be described by simple maps for the intensity operators.

18 pages, 1 figure. v5: accepted by Quantum

References in corpus (8)

• The Quantum Chernoff Bound
• The Chernoff lower bound for symmetric quantum hypothesis testing
• Quantum Fisher Information with Coherence
• Quantum limits of superresolution in a noisy environment
• Experimental demonstration of superresolution of partially coherent light sources using parity sorting
• Subwavelength quantum imaging with noisy detectors
• Effects of coherence on temporal resolution
• Generalization of Rayleigh's Criterion on Parameter Estimation with Incoherent Sources

Cited by in corpus (9)

• Linear optics and photodetection achieve near-optimal unambiguous coherent state discrimination
• Back to sources -- the role of losses and coherence in super-resolution imaging revisited
• Quantum limit to subdiffraction incoherent optical imaging. II. A parametric-submodel approach
• Quantum limits for resolving Gaussian sources
• Efficient superoscillation measurement for incoherent optical imaging
• Quantum limit to subdiffraction incoherent optical imaging. III. Numerical analysis
• Measuring the Oscillation Frequency Beyond the Diffraction Limit
• Efficient lineshape estimation by ghost spectroscopy
• Quantum-limited superresolution of two arbitrary incoherent point sources: beating the resurgence of Rayleigh's curse