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Investigation of Momogamy Relations and Their Inequalities in Multipartite Quantum Systems

Zahra Feizi Chanaghblaghi

Published Jan 1, 2017• 0 citations
OpenAlex

Abstract

As the quantum entangled states are as a source for many of branches different quantum information theory, such as dense encoding,encryption and teleportation, theoretical study of any relation between the different parts of a entangled quantum state of semi-transparent. One of these relations, inequality monogamy. Although the correlation classical can be freely in the multipartite systems will be shared, the famous that quantum entanglement in this share has restrictions. This restriction on the sharing of entanglement, the famous to monogamy in the multipartite quantum systems. In terms of math, monogamy in the entanglement the first was introduced by Coffman-Kundu-Wootters (CKW) in the three qubit systems. Inequality CKW that obtained for the measure concurrence, mutually unique nature of entanglement two qubits common in the three qubit systems shows. A simple example of the monogamy property can be expressed that the amount of entanglement between A and B to add the amount of entanglement between A and C cannot be greater than the amount of entanglement between A and pair BC. The aim of this thesis reviews the types monogamy inequality defined for the various entangled measures especially measure concurrence.

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As the quantum entangled states are as a source for many of branches different quantum information theory, such as dense encoding,encryption and teleportation, theoretical study of any relation between the different parts of a entangled quantum state of semi-transparent. One of these relations, inequality monogamy. Although the correlation classical can be freely in the multipartite systems will be shared, the famous that quantum entanglement in this share has restrictions. This restriction on the sharing of entanglement, the famous to monogamy in the multipartite quantum systems. In terms of math, monogamy in the entanglement the first was introduced by Coffman-Kundu-Wootters (CKW) in the three qubit systems. Inequality CKW that obtained for the measure concurrence, mutually unique nature of entanglement two qubits common in the three qubit systems shows. A simple example of the monogamy property can be expressed that the amount of entanglement between A and B to add the amount of entanglement between A and C cannot be greater than the amount of entanglement between A and pair BC. The aim of this thesis reviews the types monogamy inequality defined for the various entangled measures especially measure concurrence.
Unlike classical correlation, quantum entanglement cannot be freely shared among many parties. This restricted shareability of entanglement among multi-party systems is known as monogamy of entanglement, which is one of the most fundamental properties of entanglement. Here, we summarize recent theoretical progress in the field of monogamy of entanglement. We firstly review the standard CKW-type monogamy inequalities in terms of various entanglement measures. In particular, the squashed entanglement and one-way distillable entanglement are monogamous for arbitrary dimensional systems. We then introduce some generalized version of monogamy inequalities which extend and sharpen the traditional ones. We also consider the dual polygamy inequalities for multi-party systems. Moreover, we present two new definitions to define monogamy of entanglement. Finally, some challenges and future directions for monogamy of entanglement are highlighted.
There is an interesting property about multipartite entanglement, called the monogamy of entanglement. The property can be shown by the monogamy inequality, called the Coffman–Kundu–Wootters inequality [Phys. Rev. A 61, 052306 (2000); Coffman–Kundu–WoottersPhys. Rev. Lett. 96, 220503 (2006)], and more explicitly by the monogamy equality in terms of the concurrence and the concurrence of assistance, CA(BC)2=CAB2+(CACa)2, in the three-qubit system. In this paper, we consider the monogamy equality in 2⊗2⊗d quantum systems. We show that CA(BC)=CAB if and only if CACa=0 and also show that if CA(BC)=CACa, then CAB=0, while there exists a state in a 2⊗2⊗d system such that CAB=0 but CA(BC)>CACa.
It is well known that a particle cannot freely share entanglement with two or more particles. This restriction is generally called monogamy. However the formal quantification of such restriction is only known for some measures of entanglement and for two-level systems. The first and broadly known monogamy relation was established by Coffman, Kundu, and Wootters for the square of the concurrence. Since then, it is usually said that the entanglement of formation is not monogamous, as it does not obey the same relation. We show here that despite that, the entanglement of formation cannot be freely shared and therefore should be said to be monogamous. Furthermore, the square of the entanglement of formation does obey the same relation of the squared concurrence, a fact recently noted for three particles and extended here for N particles. Therefore the entanglement of formation is as monogamous as the concurrence. We also numerically study how the entanglement is distributed in pure states of three qubits and the relation between the sum of the bipartite entanglement and the classical correlation.
Quantum entanglement for multiparty system has a unique feature when it comes to sharing its property among various subsystems. This is famously stated as the monogamy of entanglement. The traditional monogamy of concurrence for tripartite system was proved in a sum form. Recently, it was found that concurrence also respects a monogamy in the product form. Here, we prove a tight monogamy relation in the product form for the concurrence of pure tripartite systems. We illustrate our relation with several examples, including the canonical three qubit states, where this monogamy relation is saturated.
We investigate possible generalizations of the Coffman-Kundu-Wootters monogamy inequality to four qubits, accounting for multipartite entanglement in addition to the bipartite terms. We show that the most natural extension of the inequality does not hold in general, and we describe the violations of this inequality in detail. We investigate alternative ways to extend the monogamy inequality to express a constraint on entanglement sharing valid for all four-qubit states, and perform an extensive numerical analysis of randomly generated four-qubit states to explore the properties of such extensions.
Abstract Quantum entanglement in multipartite systems exhibits a unique restriction on its distribution among subsystems, a fundamental property known as the monogamy of entanglement. Traditionally, monogamy has been quantified for measures such as concurrence through summation-form inequalities. Recently, it has been discovered that concurrence also obeys monogamy constraints expressed via product-form inequalities. In this work, we establish enhanced monogamy inequalities for the ν th power of concurrence (with ν ⩾ 2 ). We demonstrate, through explicit examples, that these new inequalities provide tighter bounds than existing product-form results. Furthermore, we show that our findings remain applicable to monogamy relations in high-dimensional systems.