Shareability of Quantum Steering and its Relation with Entanglement

Abstract

Steerability is a characteristic of quantum correlations lying in between entanglement and Bell nonlocality. Understanding how these steering correlations can be shared between different parties has profound applications in ensuring security of quantum communication protocols. Here we show that at most two bipartite reduced states of a three qubit state can violate the three settings CJWR linear steering inequality contrary to two settings linear steering inequality. This result explains that quantum steering correlations have limited shareability properties and can sometimes even be nonmonogamous. In contrast to the two setting measurement scenario, three setting scenario turns out to be more useful to develop deeper understanding of shareability of tripartite steering correlations. Apart from distribution of steering correlations, several relations between reduced bipartite steering, different measures of bipartite entanglement of reduced states and genuine tripartite entanglement are presented here. The results enable detection of different kind of tripartite entanglement.

13 pages, 1 figure

References in corpus (25)

• The Quantum Internet
• Entanglement detection
• Steering, Entanglement, Nonlocality, and the EPR Paradox
• General Monogamy Inequality for Bipartite Qubit Entanglement
• Experimental criteria for steering and the Einstein-Podolsky-Rosen paradox
• Quantum Steering
• Entanglement, EPR-correlations, Bell-nonlocality, and Steering
• Einstein-Podolsky-Rosen steering provides the advantage in entanglement-assisted subchannel discrimination with one-way measurements
• Is Entanglement Monogamous?
• A classification of entanglement in three-qubit systems
• Entanglement monogamy relations of qubit systems
• Einstein-Podolsky-Rosen steering and the steering ellipsoid
• Analog of the Clauser-Horne-Shimony-Holt inequality for steering
• Concurrence and a proper monogamy inequality for arbitrary quantum states
• Monogamy of Bell's inequality violations in non-signaling theories
• Geometric Bell-like inequalities for steering
• Quantifying the nonlocality of GHZ quantum correlations by a bounded communication simulation protocol
• Volume monogamy of quantum steering ellipsoids for multi-qubit systems
• Anisotropic invariance and the distribution of quantum correlations
• Detecting genuine multipartite entanglement of pure states with bipartite correlations
• Maximally dense coding capable quantum states
• Monogamy of particle statistics in tripartite systems simulating bosons and fermions
• Bell monogamy relations in arbitrary qubit networks
• Trade-offs in multi-party Bell inequality violations in qubit networks
• Monogamy relations for nonclassical correlations of multi-qubit states

Cited by in corpus (9)

• Demonstrating shareability of multipartite Einstein-Podolsky-Rosen steering
• Complementary relations of entanglement, coherence, steering and Bell nonlocality inequality violation in three-qubit states
• Quantum Correlation Sharing: A Review On Recent Progress From Nonlocality To Other Non-Classical Correlations
• Unification of quantum resources in tripartite systems
• Shareability of steering in 2-producible states
• Can NSI affect non-local correlations in neutrino oscillations?
• Sharing EPR steering between sequential pairs of observers
• Steering in Neutrino Oscillations with Non-Standard Interaction
• Tripartite entanglement and tripartite steering in three-qubit pure states induced by vacuum--one-photon superpositions