Monogamy of quantum entanglement

2022/01/02 by Xiao-Lan Zong, Hao-Hao Yin, Wei Song +2 · 1 voice · 12 citations
Computer Science · Mathematics · Physics and Astronomy · #Computer science #Field (mathematics) #Mathematics #Multipartite entanglement #Physics #Pure mathematics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum entanglement #Quantum mechanics #Squashed entanglement #Theoretical physics #quant-ph

paper · pdf · open access · doi:10.3389/fphy.2022.880560

published in Frontiers in Physics 10 (Frontiers Media) · 8 pages,1 figure,a short review

arxiv published 2022/01/02 · openalex publication_date 2022/06/09 · arxiv created 2022/06/18 · arxiv updated 2022/06/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

Abstract

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.

Citations

• Why entanglement of formation is not generally monogamous
• Three qubits can be entangled in two inequivalent ways
• Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels
• Logarithmic Negativity: A Full Entanglement Monotone That is not Convex
• Continuous variable tangle, monogamy inequality, and entanglement sharing in Gaussian states of continuous variable systems
• Is entanglement monogamous?
• Generalized W-class state and its monogamy relation
• Mixed-State Entanglement and Distillation: Is there a “Bound” Entanglement in Nature?
• Entanglement of Formation of an Arbitrary State of Two Qubits
• Separability Criterion for Density Matrices
• Strong Monogamy of Bipartite and Genuine Multipartite Entanglement: The Gaussian Case
• Deterministic entanglement of assistance and monogamy constraints
• Monogamy and entanglement in tripartite quantum states
• Entanglement of a Pair of Quantum Bits
• Monogamy Inequality for Distributed Gaussian Entanglement
• Entanglement of Distillation and Conditional Mutual Information
• Separability of mixed states: necessary and sufficient conditions
• Tsallis entropy and entanglement constraints in multiqubit systems
• Strong monogamy inequalities for four qubits
• Distributed Entanglement

Discussions

• This is actually an excellent question, and the answer itself is very important to understand when considering spacetime extended entangled quantum systems. First, the cited experiment is important be [stackexchange, 2 points]

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• Measure of entanglement and the monogamy relation: a topical review