Information-theoretic measure of genuine multiqubit entanglement

Abstract

We consider pure quantum states of N qubits and study the genuine N −qubit entanglement that is shared among all the N qubits. We introduce an information-theoretic measure of genuine N -qubit entanglement based on bipartite partitions. When N is an even number, this measure is presented in a simple formula, which depends only on the purities of the partially reduced density matrices. It can be easily computed theoretically and measured experimentally. When N is an odd number, the measure can also be obtained in principle.PACS numbers: 03.67.-a, 03.65. Ud, 73.43.Nq, 89.70.+c The nature of quantum entanglement is a fascinating topic in quantum mechanics since the famous EinsteinPodolsky-Rosen paper [1] in 1935. Recently, much interest has been focused on entanglement in quantum systems containing a large number of particles. On one hand, multipartite entanglement is valuable physical resource in large-scale quantum information processing [2,3]. On the other hand, multipartite entanglement seems to play an important role in condensed matter physics [4], such as quantum phase transitions (QPT) [5,6] and high temperature superconductivity [7]. Therefore, how to characterize and quantify multipartite entanglement remains one of the central issues in quantum information theory.In the present literature, there exist very few measures of multipartite entanglement with a clear physical meaning [8,9,10,11,12,13,14,15]. Because of this, most research in quantum entanglement and QPT focused on bipartite entanglement, for which there have been several well defined measures [16,17,18,19,20,21,22]. However, bipartite entanglement can not characterize the global quantum correlations among all parties in a multiparticle system. Since the correlation length diverges at the critical points, multipartite entanglement plays an essential role in QPT. Though localizable entanglement (LE) [23] can be used to describe long-range quantum correlations, its determination is a formidable task for generic pure states. Therefore, computable measure of multipartite entanglement with clear physical meanings are highly desired [24,25].In this paper, we define a new measure of genuine N −qubit entanglement based on different bipartite partitions of the qubits and existing measures for mutual information. The central idea is that, through bipartite partitions, we can get information about the genuine multi-qubit entanglement. Our measure is a polynomial SLOCC (stochastic local operations and classical communication) invariant [26] and is unchanged under permutations of qubits. When N is an even number, we derive * Electronic address: zwzhou@ustc.edu.cn a simple formula for this measure, which is determined by the purity of partially reduced density matrices only. It can be computed through experimentally observable quantities [10,27]. Therefore, it is easy to obtain not only theoretically but also experimentally. For N = 4, we show that this measure satisfies all the necessary conditions required for a natural entanglement measure [20] exactly....

Perfect quantum transport in arbitrary spin networks

“…6 shows the scaling of the transport time between two separated NV centers via a bulk network consisting of randomly positioned nitrogen impurities (P1 centers). Transport fidelity loss could occur due to dipolar induced decoherence 44,45 . Dephasing times in excess of 100µs are routinely achievable in diamond 46,47 .…”

Quantum correlations in quenched disordered spin models: Enhanced order from disorder by thermal fluctuations

“…Defects can also be modeled, by introducing non-uniform tuning parameters or allowing coupling between random sites [1][2][3][4][5][6]. Intuitively, one expects that disorder would reduce the properties like magnetization and conductivity of a system, and this is indeed true for a large variety of systems [7][8][9][10][11][12][13][14][15][16]. However, there are examples of certain systems, both classical as well as quantum, in which properties like magnetization, classical correlators, entanglement get enhanced with the introduction of disorder -the phenomena are termed as order-from-disorder [8,9,[17][18][19][20][21][22].…”

Anderson localisation in spin chains for perfect state transfer

“…b e-mail: mpee500@york.ac.uk c e-mail: irene.damico@york.ac.uk d e-mail: timothy.spiller@york.ac.uk it can be conjectured that long chains would be the most affected by random fabrication defects [20][21][22][23][24][25][26] or by slowly varying external fields. Within this context, we have investigated the question of if and how random defects would affect the relevant transmission properties of PST spin chains, through the appearance of weak localisation or Anderson localisation.…”