Analytic Semi-device-independent Entanglement Quantification for Bipartite Quantum States
arXiv:1903.05303 · doi:10.1103/PhysRevA.103.032215
Abstract
We define a property called nondegeneracy for Bell inequalities, which describes the situation that in a Bell setting, if a Bell inequality and involved local measurements are chosen and fixed, any quantum state with a given dimension and its orthogonal quantum state cannot violate the inequality remarkably at the same time. By choosing a proper nondegenerate Bell inequality, we prove that for a unknown bipartite quantum state of a given dimension, based on the measurement statistics only, we can provide an analytic lower bound for the entanglement of formation or even for the distillable entanglement, making the whole process semi-device-independent. We characterize the mathematical structure of nondegenerate Bell inequalities, and prove that quite a lot of well-known Bell inequalities are nondegenerate. We demonstrate our approach by quantifying entanglement for qutrit-qutrit states based on their violation to the CGLMP inequality.
A mathematical characterization for nondegeneracy Bell inequalities that proves quite a lot of well-known Bell inequalities are nondegenerate was added; A demonstration of our approach that quantifies the entanglement of qutrit-qutrit states based on their violation to the CGLMP inequality was also provided; Comments are welcome
References in corpus (15)
- SciPy 1.0--Fundamental Algorithms for Scientific Computing in Python
- Entanglement detection
- Probing entanglement entropy via randomized measurements
- Bounding the set of quantum correlations
- Geometry of the set of quantum correlations
- Imperfect measurements settings: implications on quantum state tomography and entanglement witnesses
- Measuring the Renyi entropy of a two-site Fermi-Hubbard model on a trapped ion quantum computer
- Entanglement irreversibility from quantum discord and quantum deficit
- Semi-device-independent bounds on entanglement
- Device-independent detection of genuine multipartite entanglement for all pure states
- Semi-device-independent characterisation of multipartite entangled states and measurements
- Device-independent Certification of One-shot Distillable Entanglement
- Experimental semi-device-independent certification of entangled measurements
- Measurement-device-independent quantification of irreducible high-dimensional entanglement
- Quantifying Coherence and Entanglement via Simple Measurements