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Physical Review A

Inference schemes and entanglement determination

Josep Amengual i Batle, M. Casas, Angel Ricardo Plastino, Angel Ricardo Plastino

Published Jan 15, 2002• 5 citations
Publisher

Abstract

The problem of inferring entanglement on the basis of incomplete prior information [R. Horodecki et al., Phys. Rev. A 59, 1799 (1999)] is reexamined with regard to operators of a more general character than the ones discussed by these authors. We show that different inference schemes are affected by the problem of overestimating the amounts of entanglement (AOE). For bipartite quantum systems, states containing the maximum and minimum possible AOE are derived explicitly.

DOI
10.1103/physreva.65.024304

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The problem of inferring entanglement on the basis of incomplete prior information [R. Horodecki et al., Phys. Rev. A 59, 1799 (1999)] is reexamined with regard to operators of a more general character than the ones discussed by these authors. We show that different inference schemes are affected by the problem of overestimating the amounts of entanglement (AOE). For bipartite quantum systems, states containing the maximum and minimum possible AOE are derived explicitly.
The inference of entangled states on the basis of incomplete prior information is usually affected by the problem of fake inferred entanglement. We show that different inferences schemes overestimate the amount of entanglement. However, the Maximum-Entropy Minimum-Norm method yields all the accessible states compatible with the prior information of the system. For bipartite systems the entanglement boundaries are explicitly determined when the knowledge of the system is restricted to the expectation value of a generic operator diagonal in the Bell basis.
The inference of entangled quantum states by recourse to the maximum entropy (MaxEnt) principle is considered in connection with the recently pointed out problem of fake inferred entanglement (Horodecki R et al 1999 Phys. Rev. A 59 1799). We show that there are operators Â, both diagonal and non-diagonal in the Bell basis, such that, when the expectation value ⟨Â⟩ is taken as prior information, the problem of fake entanglement is not solved by adding a new constraint associated with the mean value of  2 (unlike what happens when the partial information is given by the expectation value of a Bell operator). The fake entanglement generated by the MaxEnt principle is also studied quantitatively by comparing the entanglement of formation of the inferred state with that of the original one.
The inference of entangled quantum states by recourse to the maximum entropy (MaxEnt) principle is considered in connection with the recently pointed out problem of fake inferred entanglement (Horodecki R et al 1999 Phys. Rev. A 59 1799). We show that there are operators Â, both diagonal and non-diagonal in the Bell basis, such that, when the expectation value  is taken as prior information, the problem of fake entanglement is not solved by adding a new constraint associated with the mean value of Â2 (unlike what happens when the partial information is given by the expectation value of a Bell operator). The fake entanglement generated by the MaxEnt principle is also studied quantitatively by comparing the entanglement of formation of the inferred state with that of the original one.