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Journal of Physics A Mathematical and Theoretical

Three-tangle rate controlled by local operation

Shun Zhang, Zheng-Wei Zhou, Chengjie Zhang, Guang‐Can Guo

Published Jan 21, 2009• 0 citations
Publisher

Abstract

Since local unitary operations do not change any entanglement measures, to manipulate the distribution of multipartite entanglement, non-local unitary operations should be required. Given a three-qubit system, we study the change of three-tangle under bipartite unitary evolution. We find, once the form of a bipartite interaction is fixed, the changing rate of three-tangle depends on additional single-qubit unitary operations. Furthermore, we give an explicit definition of the three-tangle rate controlled by local operations. By taking advantage of this three-tangle rate, we discuss three examples.

DOI
10.1088/1751-8113/42/7/075304

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Since local unitary operations do not change any entanglement measures, to manipulate the distribution of multipartite entanglement, non-local unitary operations should be required. Given a three-qubit system, we study the change of three-tangle under bipartite unitary evolution. We find, once the form of a bipartite interaction is fixed, the changing rate of three-tangle depends on additional single-qubit unitary operations. Furthermore, we give an explicit definition of the three-tangle rate controlled by local operations. By taking advantage of this three-tangle rate, we discuss three examples.
The entanglement production is key for many applications in the realm of quantum information, but so is the identification of processes that allow to create entanglement in a fast and sustained way. Most of the advances in this direction have been circumscribed to bipartite systems only, and the rate of entanglement in multipartite system has been much less explored.Here we contribute to the identification of processes that favor the fastest and sustained generation of tripartite entanglement in a class of 3-qubit GHZ-type states. By considering a three-party interaction Hamiltonian, we analyse the dynamics of the 3-tangle and the entanglement rate to identify the optimal local operations that supplement the Hamiltonian evolution in order to speed-up the generation of three-way entanglement, and to prevent its decay below a predetermined threshold value. The appropriate local operation that maximizes the speed at which a highly-entangled state is reached has the advantage of requiring access to only one of the qubits, yet depends on the actual state of the system. Other universal (state-independent) local operations are found that conform schemes to maintain a sufficiently high amount of 3-tangle. Our results expand our understanding of entanglement rates to multipartite systems, and offer guidance regarding the strategies that improve the efficiency in various quantum information processing tasks.
Abstract The entanglement production is key for many applications in the realm of quantum information, but so is the identification of processes that allow to create entanglement in a fast and sustained way. Most of the advances in this direction have been circumscribed to bipartite systems only, and the rate of entanglement in multipartite system has been much less explored. Here we contribute to the identification of processes that favor the fastest and sustained generation of tripartite entanglement in a class of 3-qubit GHZ-type states. By considering a three-party interaction Hamiltonian, we analyze the dynamics of the 3-tangle and the entanglement rate to identify the optimal local operations that supplement the Hamiltonian evolution in order to speed-up the generation of three-way entanglement, and to prevent its decay below a predetermined threshold value. The appropriate local operation that maximizes the speed at which a highly-entangled state is reached has the advantage of requiring access to only one of the qubits, yet depends on the actual state of the system. Other universal (state-independent) local operations are found that conform schemes to maintain a sufficiently high amount of 3-tangle. Our results expand our understanding of entanglement rates to multipartite systems, and offer guidance regarding the strategies that improve the efficiency in various quantum information processing tasks.
In this paper, we are focusing on entanglement control problem in a three-qubit system. We demonstrate that vector representation of entanglement, associated with SO(6) representation of SU(4) two-qubit group, can be used to solve various control problems analytically including ( i) the transformation between a W-type states and GHZ state, and ( ii) manipulating bipartite concurrences and three-tangle under a restricted access to only two qubits, and ( iii) designing USp(4)-type quaternionic operations and quantum states.
Multipartite entanglement is an indispensable resource in quantum communication and computation; however, it is a challenging task to faithfully quantify this global property of multipartite quantum systems. In this work we study the concurrence fill, which admits a geometric interpretation to measure genuine tripartite entanglement for the three-qubit system [Xie and Eberly, Phys. Rev. Lett. 127, 040403 (2021)]. First, we use the well-known three-tangle and bipartite concurrence to reformulate this quantifier for all pure states. We then construct an explicit example to conclusively show that the concurrence fill can be increased under local operations and classical communication (LOCC) on average, implying it is not an entanglement monotone. Moreover, we give a simple proof of the LOCC monotonicity of the three-tangle and find that the bipartite concurrence and the squared concurrence can have distinct performances under the same LOCC. Finally, we propose a reliable monotone to quantify genuine tripartite entanglement, which can also be easily generalized to the multipartite system. Our results shed light on the study of genuine entanglement and also reveal the complex structure of multipartite systems.