Revealing hidden physical nonclassicality with nonnegative polynomials
arXiv:2403.09807 · doi:10.1103/PhysRevLett.134.030201
Abstract
Understanding quantum phenomena which go beyond classical concepts is a focus of modern quantum physics. Here, we show how the theory of nonnegative polynomials emerging around Hilbert's 17th problem, can be used to optimally exploit data capturing the nonclassical nature of light. Specifically, we show that nonnegative polynomials can reveal nonclassicality in data even when it is hidden from standard detection methods up to now. Moreover, the abstract language of nonnegative polynomials also leads to a unified mathematical approach to nonclassicality for light and spin systems, allowing us to map methods for one to the other. Conversely, the physical problems arising also inspire several mathematical insights into characterisation of nonnegative polynomials.
17 pages, 5 figures, published version
References in corpus (11)
- Entanglement detection
- A complete family of separability criteria
- Characterizing the entanglement of symmetric many-particle spin-1/2 systems
- Entanglement and permutational symmetry
- Experimental determination of a nonclassical Glauber-Sudarshan P function
- Semidefinite Programming in Quantum Information Science
- Separability of diagonal symmetric states: a quadratic conic optimization problem
- Atomic nonclassicality quasiprobabilities
- Nonlocality and Entanglement for Symmetric States
- Balanced homodyne detection with on-off detector systems: Observable nonclassicality criteria
- Tensor eigenvalues and entanglement of symmetric states