Quantifying entanglement with witness operators
By Fernando G. S. L. Brandão. 2005
193 citations recorded by the source corpus.
We present a unifying approach to the quantification of entanglement based on entanglement witnesses, which includes several already established entanglement measures such as the negativity, the concurrence, and the robustness of entanglement. We then introduce an infinite family of new entanglement quantifiers, having as its limits the best separable approximation measure and the generalized robustness. Gaussian states, states with symmetry, states constrained to super-selection rules, and states composed of indistinguishable particles are studied under the view of the witnessed entanglement. We derive new bounds to the fidelity of teleportation d_(min), for the distillable entanglement E_D and for the entanglement of formation. A particular measure, the PPT-generalized robustness, stands out due to its easy calculability and provides sharper bounds to d_(min) and E_D than the negativity in most of the states. We illustrate our approach studying thermodynamical properties of entanglement in the Heisenberg XXX and dimerized models.
Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics
View Paper: https://www.semanticscholar.org/paper/96a6e0fe3f5962f9d34cf789424790b41bed9d4b
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In Artificial Intelligence
In Atomic and Molecular Physics, and Optics
Citations in the corpus
- Entanglement detection (2008, background): “Therefore, one considers the quantity [423]”
- Faithful Squashed Entanglement (2010, unknown): “• The maximum gap in expectation value for an entangled state versus separable states, optimised over all witnesses from a class M, is equal to the minimum distance of the entangled state to the set of separable states in the M norm and thus can also be used to quantify the entanglement of the state”
- Quantum coherence and geometric quantum discord (2017, background): “By minimizing over the compact subsetM of the set of entanglement witnesses W, one can obtain the optimal entanglement witness, and define the quantifier Ew(ρ) = max{0,− min W∈M tr(Wρ)}, (38) as an entanglement measure (Brandão, 2005).”