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Frontiers in Optics

Bipartite and Tripartite Entanglement for Three Damped Driven Qubits

Habtom Woldekristos, Bill J. Konyk, James Clemens, Perry R. Rice

Published Jan 1, 2012• 0 citations
Publisher

Abstract

, We investigate tripartite entanglement in an open quantum system, specifically three qubits, all of which are damped, and one of which is driven. We address a systematic approach in calculating the entanglement of various bipartite splits using concurrence as a measure of entanglement Our calculations are based on a direct detection scheme (quantum jump method - with and without knowledge of which qubit jumps) that is a particular unravelling of the density matrix. Our results are unravelling dependent, but apply to applications of entanglement based on direct detection. We also calculate the ’Three-way tangle’ or ’Residual Entanglement’ for this system. We present calculations for a variety of driving and damping rates, and examine what decay rate is adequate for the system to be reduced to two qubits with a readout port. We also consider how knowledge (or not) of which qubit decays affects the entanglement.

DOI
10.1364/ls.2012.lw1j.1

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, We investigate tripartite entanglement in an open quantum system, specifically three qubits, all of which are damped, and one of which is driven. We address a systematic approach in calculating the entanglement of various bipartite splits using concurrence as a measure of entanglement Our calculations are based on a direct detection scheme (quantum jump method - with and without knowledge of which qubit jumps) that is a particular unravelling of the density matrix. Our results are unravelling dependent, but apply to applications of entanglement based on direct detection. We also calculate the ’Three-way tangle’ or ’Residual Entanglement’ for this system. We present calculations for a variety of driving and damping rates, and examine what decay rate is adequate for the system to be reduced to two qubits with a readout port. We also consider how knowledge (or not) of which qubit decays affects the entanglement.
We investigate bipartite and tripartite entanglement in an open quantum system, specifically three qubits, all of which are damped, and one of which is driven. We adapt a systematic approach in calculating the entanglement of various bipartite splits usinga generalized concurrence as an indicator of entanglement. Our calculations are based on a direct detection scheme that is a particular unravelling of the density matrix. This system has a collective dipole-dipole energy shift that couples the atoms and the dissipation is via partially collective spontaneous emission described by the Lehmberg-Agarwal master equation.Our results are unravelling dependent, but apply to applications of entanglement based on direct detection. We also calculate the three-way tangle or residual entanglement for this system. We present calculations for a variety of driving and damping rates, and examine what decay rate is adequate for the system to be reduced to two qubits with a readout port. We also consider a specific model of three atoms located at particular positions in free space.
’We investigate entanglement in an open quantum system, specifically in bipartite and tripartite systems of two dimensions for weak and strong fields based on numerical calculations. We address a systematic approach in calculating a tripartite entanglement using concurrence as a measure of entanglement based on a direct detection scheme (quantum jump method - with and without knowledge of which qubit jumps). We are also numerically calculating entanglement when one can and the ’Three-way tangle’ or ’Residual Entanglement’ approaches. We present significant differences of the concurrences of the various bipartite splits among the results of two ways of direct detection scheme and when a phase is introduced in the coupling term of the energy.
By applying a modified conjugate gradient method in the evaluation of three-qubit residual entanglement, the disentanglement of three-qubit states in an amplitude-damping and dephasing environment is investigated numerically. It is found that the decay of tripartite entanglement is faster than bipartite entanglement in the same qubits-noise system, which indicates that multipartite entanglement is more fragile than bipartite entanglement in resisting quantum noises. Similar to the case of a two-qubit system, three-qubit entanglement subject to an open environment may also disappear abruptly (sudden death) or decrease asymptotically, which is dependent on the conditions of the initially entangled quantum state and the properties of quantum noise.
Quantum entanglement is the fundamental hallmark of quantum mechanics and a core resource for realizing long-distance quantum communication and scalable linear quantum computing. Accordingly, the precise detection and quantitative quantification of entanglement constitute a foundational and critical problem in quantum information theory. To date, researchers have proposed numerous sufficient conditions for entanglement detection as well as a variety of entanglement measures to characterize the entanglement strength of quantum states; nevertheless, efficient and direct measurement schemes for core entanglement parameters remain underdeveloped. Based on unitary transformations and auxiliary measurements, this paper proposes a set of quantum circuit schemes capable of directly measuring the bipartite concurrence and the tripartite 3-tangle entanglement measure. By introducing auxiliary qubits and constructing specific controlled unitary operations, the proposed scheme maps the analytical expressions of the two entanglement measures onto the measurement probabilities of output states from quantum circuits. It enables efficient and direct quantitative measurement of bipartite and tripartite entanglement without performing full quantum state tomography. This work provides a feasible technical route for the experimental characterization of entanglement properties and lays a groundwork for the practical deployment of multipartite entanglement resources in quantum information processing.
This study presents an analytical investigation of entanglement quantification in three-qubit pure states through the Acín canonical representation, which serves as a generalization of the two-qubit Schmidt decomposition. Driven by the intricacies of multipartite entanglement and the shortcomings of current measures, we employ a global concurrence measure derived from the generalized concurrence of various bipartitions within the system. The characteristics of this measure are explored both analytically and numerically across a range of SLOCC entanglement classes, such as product, biseparable, GHZ-type, and W-type states. When compared to the three-tangle and tripartite negativity, our findings indicate that this measure yields complementary insights into multipartite correlations. The outcomes underscore the significance of this measure in elucidating the structure and distribution of entanglement within three-qubit quantum systems.