Entanglement of linear cluster states in terms of averaged entropies

Abstract

An entanglement measure, multiple entropy measures (MEMS) was proposed recently by using the geometric mean of partial entropies over all possible i-body combinations of the quantum system. In this work, we study the average subsystem von Neumann entropies of the linear cluster state and investigated the quantum entanglement of linear cluster states in terms of MEMS. Explicit results with specific particle numbers are calculated, and some analytical results are given for systems with arbitrary particle numbers. Compared with other example quantum states such as the GHZ states and W states, the linear cluster states are "more entangled" in terms of MEMS, namely their averaged entropies are larger than the GHZ states and W states. Entanglement [1, 2] is one of the most salient properties of quantum systems. Quantum entanglement led to the experimental verification for Bell inequality which confirmed quantum mechanics [3]. In recent years, quantum entanglement has been one of the key driving forces that advanced the explosive development of quantum information and quantum computation [4][5][6][7][8][9][10][11][12]. Entanglement has developed from a philosophical concept into a frontier research paradigm, and much more attention has been paid to the quantification of entanglement. Two measures of entanglement, formation and distillation [15,16] were also studied and recognized as "good" entanglement measures.In studying quantum entanglement, the density matrices are often used. It should be mentioned that density matrix can represent different physical quantities. In the case of proper mixture, the density matrix represents the averaged "state" of an ensemble of "molecules", while the improper mixture describes the averaged "state" of a subsystem in a coupled quantum system. Though the mathematical expressions are the same, their physical properties are quite differ-*Corresponding author (email: gllong@mail.tsinghua.edu.cn) ent [49,50]. In studying quantum entanglement, we are actually using the improper mixture meaning of the density matrix. The reduced density matrix is obtained by tracing out other degrees of freedom of a composite quantum system. Based on separating the correlations encoded by a density matrix into a common set of marginals, Partovi [37] proposed a measurement in which N!/2 quantities are used to quantify an N-qubit system. In the case of N 3, a "good" measurement [38] can be constructed from the arithmetic average entropy of single reduced density matrices. Realizing the lack of one-qubit reduction, Higuchi et al. [51,52] proposed using the arithmetic mean of two-particle entropies as a measure of entanglement, and reported on a four-qubit entangled state:which is more entangled than the four-qubit GHZ state.

Concentration and distribution of entanglement based on valley qubits system in graphene

“…Furthermore, the proposed system can be designed to realize universal quantum logic gate [34] which could be applied in quantum computers [35,36]. Moreover, the solid qubits entangled system could be used to study the characterization the entanglement [37][38][39]. Also recent process on entanglement concentration using QDs and cavity coupled system [40,41] has been proposed; the proposed protocol is based on the input-output relation of single photon in single QD and cavity coupled system.…”

Quantum phase transitions in matrix product states of one-dimensional spin-1 chains

“…Now, let us study the entanglement property of the MPS, the key quantity of quantum information theory [12][13][14][15], in detail. About measures of entanglement there are many kinds of methods, such as the quantification characteristic function of quantum nonlocality [16], Bell inequality [17,18], quantum discord [19], averaged entropy [20] and so on. Considering our system, we shall adopt the von Neumann entropy which [21][22][23][24][25][26][27][28] according to bipartition parameterization by the adjacent spin number n of a B n spin block is,…”

Quantum phase transitions in matrix product states of one-dimensional spin-½ chains

“…Now, let us study the entanglement property of the MPS, the key quantity of quantum information theory [14][15][16][17], in detail. There are many kinds of methods to measure entanglement, such as the quantification characteristic function of quantum nonlocality [18], Bell inequality [19,20], quantum discord [21], averaged entropy [22] and so on. For our system, we shall adopt the von Neumann entropy which [23][24][25][26][27][28][29][30] according to the bipartition parameterization by the adjacent spin number n of a B n spin block is,…”