Characterizing multipartite entanglement by violation of CHSH inequalities

Abstract

Entanglement of high-dimensional and multipartite quantum systems offer promising perspectives in quantum information processing. However, the characterization and measure of such kind of entanglement is of great challenge. Here we consider the overlaps between the maximal quantum mean values and the classical bound of the CHSH inequalities for pairwise-qubit states in two-dimensional subspaces. We show that the concurrence of a pure state in any high-dimensional multipartite system can be equivalently represented by these overlaps. Here we consider the projections of an arbitrary high-dimensional multipartite state to two-qubit states. We investigate the non-localities of these projected two-qubit sub-states by their violations of CHSH inequalities. From these violations, the overlaps between the maximal quantum mean values and the classical bound of the CHSH inequality, we show that the concurrence of a high-dimensional multipartite pure state can be exactly expressed by these overlaps. We further derive a lower bound of the concurrence for any quantum states, which is tight for pure states. The lower bound not only imposes restriction on the non-locality distributions among the pairwise qubit states, but also supplies a sufficient condition for distillation of bipartite entanglement. Effective criteria for detecting genuine tripartite entanglement and the lower bound of concurrence for genuine tripartite entanglement are also presented based on such non-localities.

arXiv comment8 pages, 2 figures

References in corpus (33)

• Quantum entanglement
• Quantum Cryptography
• Quantum secret sharing
• Entanglement detection
• Security of quantum key distribution using d-level systems
• Mixed-state entanglement and distillation: is there a ``bound'' entanglement in nature?
• Multipartite entanglement and high precision metrology
• Entanglement and Extreme Spin Squeezing
• Quantum Cryptography using larger alphabets
• Fidelity and Concurrence of conjugated states
• Generation and Confirmation of a (100x100)-dimensional entangled Quantum System
• Taming multiparticle entanglement
• Measure of genuine multipartite entanglement with computable lower bounds
• Device-independent witnesses of genuine multipartite entanglement
• Detection of high-dimensional genuine multi-partite entanglement of mixed states
• Entanglement versus Bell violations and their behaviour under local filtering operations
• A Note on Invariants and Entanglements
• Multipartite Entanglement Witnesses
• Quantifying photonic high-dimensional entanglement
• Room-temperature implementation of the Deutsch-Jozsa algorithm with a single electronic spin in diamond
• Entanglement of three-qubit Greenberger-Horne-Zeilinger-symmetric states
• Multipartite entanglement detection from correlation tensors
• Witnessing genuine multipartite entanglement with positive maps
• Measure of multipartite entanglement with computable lower bounds
• Concurrence and a proper monogamy inequality for arbitrary quantum states
• Determining lower bounds on a measure of multipartite entanglement from few local observables
• Characterizing multipartite entanglement without shared reference frames
• Better Bell Inequality Violation by Collective Measurements
• Genuine multipartite entanglement detection and lower bound of multipartite concurrence
• Trade-off Relations of Bell Violations among Pairwise Qubit Systems
• Multipartite entanglement outperforming bipartite entanglement under limited quantum system sizes
• Detecting genuine multipartite entanglement of pure states with bipartite correlations
• Any multipartite entangled state violating Mermin-Klyshko inequality can be distilled for almost all bipartite splits