Entanglement does not correspond to an observable, and its evaluation always corresponds to an estimation procedure where the amount of entanglement is inferred from the measurements of one or more proper observables. Here we address optimal estimation of entanglement in the framework of local quantum estimation theory and derive the optimal observable in terms of the symmetric logarithmic derivative. We evaluate the quantum Fisher information and, in turn, the ultimate bound to precision for several families of bipartite states for either for qubits or continuous-variable systems and for different measures of entanglement. We found that for discrete variables, entanglement may be efficiently estimated when it is large, whereas estimation of weakly entangled states is an inherently inefficient procedure. For continuous-variable Gaussian systems the effectiveness of entanglement estimation strongly depends on the chosen entanglement measure. Our analysis makes an important point of principle and may be relevant in the design of quantum information protocols based on the entanglement content of quantum states.

Optimal estimation of entanglement / M. Genoni, P. Giorda, M. Paris. - In: PHYSICAL REVIEW A. - ISSN 1050-2947. - 78:3(2008), p. 032303.032303.

Optimal estimation of entanglement

M. Genoni;M. Paris
Ultimo
2008

Abstract

Entanglement does not correspond to an observable, and its evaluation always corresponds to an estimation procedure where the amount of entanglement is inferred from the measurements of one or more proper observables. Here we address optimal estimation of entanglement in the framework of local quantum estimation theory and derive the optimal observable in terms of the symmetric logarithmic derivative. We evaluate the quantum Fisher information and, in turn, the ultimate bound to precision for several families of bipartite states for either for qubits or continuous-variable systems and for different measures of entanglement. We found that for discrete variables, entanglement may be efficiently estimated when it is large, whereas estimation of weakly entangled states is an inherently inefficient procedure. For continuous-variable Gaussian systems the effectiveness of entanglement estimation strongly depends on the chosen entanglement measure. Our analysis makes an important point of principle and may be relevant in the design of quantum information protocols based on the entanglement content of quantum states.
continuous variable systems ; separability criterion ; quantum states ; mixed states ; mechanics ; geometry
Settore FIS/03 - Fisica della Materia
2008
Article (author)
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/52379
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