Abstract
In this review, we introduce well-known Bell inequalities, the relations between the Bell inequality and quantum separability, and the entanglement distillation of quantum states. It is shown that any pure entangled quantum state violates one of Bell-like inequalities. Moreover, quantum states that violate any one of these Bell-like inequalities are shown to be distillable. New Bell inequalities that detect more entangled mixed states are also introduced.
Highlights
The contradiction between local realism and quantum mechanics was first highlighted by the paradox of Einstein, Podolsky and Rosen (EPR) [1]
Bell inequalities are of great importance in understanding the conceptual foundations of quantum theory and investigating quantum entanglement, as they can be violated by quantum entangled states
We show that pure entangled states can be distilled from quantum mixed states that violate one of these Bell inequalities
Summary
The famous CHSH [6] inequality is a kind of improved Bell inequality that is more feasible for experimental verification. Alice and Bob, are separated spatially and share two qubits. Alice and Bob each measure a dichotomic observable with possible outcomes ±1 in one of two measurement settings: A1, A2 and B1, B2 respectively. The Bell function for the CHSH inequality has been given as [26]. According to the local hidden-variable theory, the statistical average of the Bell function must satisfy the inequality [6, 26], | B(λ) | 2, where the statistical average B(λ) = ρ(λ)B(λ)dλ with ρ(λ) the probability density distribution. The CHSH inequality says that if there exist local hidden-variable models to describe the system, the inequality. The quantum mechanical violation of the Bell inequalities has been demonstrated experimentally, e.g. The quantum mechanical violation of the Bell inequalities has been demonstrated experimentally, e.g. [28]
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