A note on Schmidt-number witnesses based on symmetric measurements

Abstract

The Schmidt number is an important kind of characterization of quantum entanglement. Quantum states with higher Schmidt numbers demonstrate significant advantages in various quantum information processing tasks. By deriving a class of k-positive linear maps based on symmetric measurements, we present new Schmidt-number witnesses of class (k + 1). By detailed example, we show that our Schmidt number witnesses identify better the Schmidt number of quantum states in high-dimensional systems. Furthermore, we note that the Fedorov ratio, which coincides with the Schmidt number for pure Gaussian states and provides a close approximation in non-Gaussian cases such as spontaneous parametric down-conversion, serves as an experimentally accessible tool for validating the proposed (k +1)-class Schmidt-number witnesses.

References in corpus (8)

• Characterizing multipartite entanglement without shared reference frames
• Characterization of Spectral Entanglement of Spontaneous Parametric-Down Conversion Biphotons
• Characterizing entanglement dimensionality from randomized measurements
• Bounding entanglement dimensionality from the covariance matrix
• Construction of efficient Schmidt number witnesses for high-dimensional quantum states
• Enhanced Schmidt number criteria based on correlation trace norms
• Schmidt number criterion via general symmetric informationally complete measurements
• Estimating the Schmidt numbers of quantum states via symmetric measurements