Separability criteria via some classes of measurements

Abstract

Mutually unbiased bases (MUBs) and symmetric informationally complete (SIC) positive operator-valued measurements (POVMs) are two related topics in quantum information theory. They are generalized to mutually unbiased measurements (MUMs) and general symmetric informationally complete (GSIC) measurements, respectively, that are both not necessarily rank 1. We study the quantum separability problem by using these measurements and present separability criteria for bipartite systems with arbitrary dimensions and multipartite systems of multi-level subsystems. These criteria are proved to be more effective than previous criteria especially when the dimensions of the subsystems are different. Furthermore, full quantum state tomography is not needed when these criteria are implemented in experiment.

References in corpus (14)

• Entanglement detection
• Deterministic secure direct communication using GHZ states and swapping quantum entanglement
• Covariance matrices and the separability problem
• Entropic uncertainty relation for mutually unbiased bases
• Quantum superposition, entanglement, and state teleportation of a microorganism on an electromechanical oscillator
• Optimal Controlled Teleportation
• Witnessing genuine multipartite entanglement with positive maps
• Entanglement detection beyond the cross-norm or realignment criterion
• Entanglement detection using mutually unbiased measurements
• Detection of genuinely entangled and non-separable $n$-partite quantum states
• On uncertainty relations and entanglement detection with mutually unbiased measurements
• Separability criteria for several classes of $n$-partite quantum states
• Dynamics and entanglement of a membrane-in-the-middle optomechanical system in the extremely-large-amplitude regime
• Entanglement detection via some classes of measurements

Cited by in corpus (7)

• Improved separability criteria via some classes of measurements
• A $(k+1)$-partite entanglement measure of $N$-partite quantum states
• Generalization of Pauli channels through mutually unbiased measurements
• Detection of the quantum states containing at most $k-1$ unentangled particles
• Detection of tripartite entanglement based on principal basis matrix representations
• The verification of a requirement of entanglement measures
• Quantum Separability Criteria Based on Symmetric Measurements