Structured Negativity: A physically realizable measure of entanglement based on structural physical approximation

Abstract

Quantification of entanglement is one of the most important problem in quantum information theory. In this work, we will study this problem by defining a physically realizable measure of entanglement for any arbitrary dimensional bipartite system $\rho$, which we named as structured negativity $(N_S(\rho ))$. We have shown that the introduced measure satisfies the properties of a valid entanglement monotone. We also have established an inequality that relate negativity and the structured negativity. For $d\otimes d$ dimensional state, we conjecture from the result obtained in this work that negativity coincide with the structured negativity when the number of negative eigenvalues of the partially transposed matrix is equal to $\frac{d(d-1)}{2}$. Moreover, we proved that the structured negativity not only implementable in the laboratory but also a better measure of entanglement in comparison to negativity. In few cases, we obtain that structure negativity gives better result than the lower bound of the concurrence obtained by Albeverio [Phys. Rev. Lett. \textbf{95}, 040504 (2005)].

8 pages, 5 figures, Accepted in Annals of Physics

References in corpus (6)

• Entanglement detection
• Quantifying Entanglement with Witness Operators
• Entangling single atoms over 33 km telecom fibre
• Structural approximations to positive maps and entanglement breaking channels
• Concurrence via entanglement witnesses
• Designing Quantum Information Processing via Structural Physical Approximation

Cited by in corpus (1)

• Physical realization of realignment criteria using structural physical approximation