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Open Systems & Information Dynamics

Energy as an Entanglement Indicator

Miłosz R. Michalski

Published Mar 1, 2011• 0 citations
Publisher

Abstract

We explore the method of constructing an entanglement witness utilising the Hamiltonian of a physical system in consideration. Already a partial knowledge of the energy spectrum allows one not only to detect entanglement in thermal equilibrium states, but also to discriminate among its various multipartite genres. We propose an efficient approximate algorithm producing a witness capable of detecting genuine n-partite entanglement. As an illustration, the method is applied to an analytically computable example of anisotropic XXZ Heisenberg chain.

DOI
10.1142/s1230161211000030

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We use entanglement witnesses to detect entanglement in the XYXYXY chain in thermal equilibrium and determine the temperature bound below which the state is detected as entangled. We consider the entanglement witness based on the Hamiltonian. Such a witness detects a state as entangled if its energy is smaller than the energy of separable states. We also consider a family of entanglement witnesses related to the entanglement negativity of the state. We test the witnesses in infinite and finite systems. We study how the temperature bounds obtained are influenced by a quantum phase transition or a disorder line in the ground state. Very strong finite-size corrections are observed in the ordered phase due to the presence of a quasidegenerate excitation. We also study the postquench states in the thermodynamic limit after a quench when the parameters of the Hamiltonian are changed suddenly. In the case of the Ising model, we find that the mixed postquench state is detected as entangled by the two methods if the parameters of the Hamiltonian before and after the quench are close to each other. We find that the two witnesses give qualitatively similar results, showing that energy-based entanglement witnesses are efficient in detecting the nearest-neighbor entanglement in spin chains in various circumstances. For other XY models, we find that the negativity-based witnesses also detect states in some parameter regions where the energy-based witness does not, in particular, if the quench is performed from the paramagnetic phase to the ferromagnetic phase and vice versa. The domains in parameter space corresponding to postquench states detected as entangled by the energy-based witness have been determined analytically, which stresses further the utility of our method.
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