Monogamy inequalities for the EPR paradox and quantum steering
arXiv:1310.2729 · doi:10.1103/PhysRevA.88.062108
Abstract
Monogamy inequalities for the way bipartite EPR steering can be distributed among N systems are derived. One set of inequalities is based on witnesses with two measurement settings, and may be used to demonstrate correlation of outcomes between two parties, that cannot be shared with more parties. It is shown that the monogamy for steering is directional. Two parties cannot independently demonstrate steering of a third system, using the same two-setting steering witness, but it is possible for one party to steer two independent systems. This result explains the monogamy of two-setting Bell inequality violations, and the sensitivity of the continuous variable (CV) EPR criterion to losses on the steering party. We generalise to m settings. A second type of monogamy relation gives the quantitative amount of sharing possible, when the number of parties is less than or equal to m, and takes a form similar to the Coffman-Kundu-Wootters (CKW) relation for entanglement. The results enable characterisation of the tripartite steering for CV Gaussian systems and qubit GHZ and W states.
10 pages, 5 figures, presented at ICSSUR Nuremberg 2013, corrections made
References in corpus (14)
- Device-independent security of quantum cryptography against collective attacks
- Steering, Entanglement, Nonlocality, and the EPR Paradox
- Multi-party entanglement in graph states
- General Monogamy Inequality for Bipartite Qubit Entanglement
- Experimental criteria for steering and the Einstein-Podolsky-Rosen paradox
- Entanglement, EPR-correlations, Bell-nonlocality, and Steering
- Observation of one-way Einstein-Podolsky-Rosen steering
- Continuous variable tangle, monogamy inequality, and entanglement sharing in Gaussian states of continuous variable systems
- Monogamy inequality for distributed Gaussian entanglement
- Unitarily localizable entanglement of Gaussian states
- Quantification and scaling of multipartite entanglement in continuous variable systems
- Experimental analysis of decoherence of quantumness in a continuous variables bi-partite entangled system
- Loss-Tolerant Tests Of Einstein-Podolsky-Rosen-Steering
- Continuous variable tripartite entanglement and Einstein-Podolsky-Rosen correlations from triple nonlinearities
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