Multi-mode entangled states represented as Grassmannian polynomials

Abstract

We introduce generalized Grassmannian representatives of multi-mode state vectors. By implementing the fundamental properties of Grassmann coherent states, we map the Hilbert space of the finite-dimensional multi-mode states to the space of some Grassmannian polynomial functions. These Grassmannian polynomials form a well-defined space in the framework of Grassmann variables; namely Grassmannian representative space. Therefore, a quantum state can be uniquely defined and determined by an element of Grassmannian representative space. Furthermore, the Grassmannian representatives of some maximally entangled states are considered, and it is shown that there is a tight connection between the entanglement of the states and their Grassmannian representatives.

A high-N00N output of harmonically driven cavity QED

“…At the heart of this quantum advantage provided by the N00N state is the quantum entanglement manifested by such a state [26,27]. Quantum entanglement, defying classical intuition, showcases the unique properties of quantum systems, which can serve as the resource for various quantum applications ranging from quantum computing to quantum communication and beyond [28,29]. In recent years, there has been a considerable effort to utilize entangled states for quantum sensing and metrology.…”