Continuous variable steering and incompatibility via state-channel duality
arXiv:1704.05734 · doi:10.1103/PhysRevA.96.042331
Abstract
The term Einstein-Podolsky-Rosen steering refers to a quantum correlation intermediate between entanglement and Bell nonlocality, which has been connected to another fundamental quantum property: measurement incompatibility. In the finite-dimensional case, efficient computational methods to quantify steerability have been developed. In the infinite-dimensional case, however, less theoretical tools are available. Here, we approach the problem of steerability in the continuous variable case via a notion of state-channel correspondence, which generalizes the well-known Choi-Jamiołkowski correspondence. Via our approach we are able to generalize the connection between steering and incompatibility to the continuous variable case and to connect the steerability of a state with the incompatibility breaking property of a quantum channel, e.g., noisy NOON states and amplitude damping channels. Moreover, we apply our methods to the Gaussian steering setting, proving, among other things, that canonical quadratures are sufficient for steering Gaussian states.
13 pages, 2 figures
References in corpus (13)
- Steering, Entanglement, Nonlocality, and the EPR Paradox
- Experimental criteria for steering and the Einstein-Podolsky-Rosen paradox
- Heisenberg's Uncertainty Principle
- Einstein-Podolsky-Rosen steering provides the advantage in entanglement-assisted subchannel discrimination with one-way measurements
- Quantum steering: a review with focus on semidefinite programming
- Quantification of Gaussian quantum steering
- Joint measurability of generalized measurements implies classicality
- Disproving the Peres conjecture: Bell nonlocality from bipartite bound entanglement
- Steering bound entangled states: A counterexample to the stronger Peres conjecture
- Schur complement inequalities for covariance matrices and monogamy of quantum correlations
- Verifying the quantumness of a channel with an untrusted device
- Sharp and fuzzy observables on effect algebras
- Channel Steering
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- Measurement-device-independent verification of channel steering
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- Diagnosing steerability of a bipartite state with the nonsteering threshold
- Divergence-free approach for obtaining decompositions of quantum-optical processes
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- Selective continuous-variable quantum process tomography
- Compressing continuous variable quantum measurements
- Entanglement Cost for Steering Assemblages
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- Quantum steerability based on joint measurability