All maximally entangled four-qubit states

Type: Article

Publication Date: 2010-11-01

Citations: 131

DOI: https://doi.org/10.1063/1.3511477

Abstract

We find an operational interpretation for the 4-tangle as a type of residual entanglement, somewhat similar to the interpretation of the 3-tangle. Using this remarkable interpretation, we are able to find the class of maximally entangled four-qubits states which is characterized by four real parameters. The states in the class are maximally entangled in the sense that their average bipartite entanglement with respect to all possible bipartite cuts is maximal. We show that while all the states in the class maximize the average tangle, there are only a few states in the class that maximize the average Tsillas or Renyi α-entropy of entanglement. Quite remarkably, we find that up to local unitaries, there exists two unique states, one maximizing the average α-Tsallis entropy of entanglement for all α ⩾ 2, while the other maximizing it for all 0 < α ⩽ 2 (including the von-Neumann case of α = 1). Furthermore, among the maximally entangled four qubits states, there are only three maximally entangled states that have the property that for two, out of the three bipartite cuts consisting of two-qubits verses two-qubits, the entanglement is 2 ebits and for the remaining bipartite cut the entanglement between the two groups of two qubits is 1 ebit. The unique three maximally entangled states are the three cluster states that are related by a swap operator. We also show that the cluster states are the only states (up to local unitaries) that maximize the average α-Renyi entropy of entanglement for all α ⩾ 2.

Locations

  • Journal of Mathematical Physics - View
  • arXiv (Cornell University) - View - PDF
  • DataCite API - View

Similar Works

Action Title Year Authors
+ PDF Chat Monogamy constraints on entanglement of four-qubit pure states 2020 S. Shelly Sharma
+ Entangled multi-qubit states without higher-tangle 2007 Heng Fan
Yong-Cheng Ou
Vwani Roychowdhury
+ Exploring maximally multipartite entanglement of even n qubits with N-tangle 2014 Xin-Wei Zha
Jianxia Qi
Yunguang Zhang
+ PDF Chat Tripartite Entanglement versus Tripartite Nonlocality in Three-Qubit Greenberger-Horne-Zeilinger-Class States 2009 Shohini Ghose
Neil Sinclair
Shantanu Debnath
Pranaw Rungta
R. Stock
+ PDF Chat Multiqubit symmetric states with maximally mixed one-qubit reductions 2014 D. Baguette
Thierry Bastin
John Martin
+ Exact monogamy constraints on entanglement of four-qubit pure states 2020 S. Shelly Sharma
+ PDF Chat Genuine entanglement of four-qubit cluster diagonal states 2013 Xiaoyu Chen
Ping Yu
Li-zhen Jiang
Mingzhen Tian
+ PDF Chat Multipartite Entanglement Measure : Genuine to Absolutely Maximally Entangled 2024 Rahul Vaze
S. Aravinda
+ Maximally entangled three-qubit states via geometric measure of entanglement 2009 Sayatnova Tamaryan
Tzu-Chieh Wei
DaeKil Park
+ PDF Chat Generalized <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>W</mml:mi></mml:math> state of four qubits with exclusively the three-tangle 2018 Sebastian Gartzke
Andreas Osterloh
+ Optimal entanglement generation in GHZ-type states 2023 Natalia Giovenale
L. Hernández-Martínez
A. P. Majtey
A. Valdés-Hernández
+ PDF Chat The maximally entangled set of 4-qubit states 2016 Cornelia Spee
Julio I. de Vicente
Barbara Kraus
+ PDF Chat Entangled Three-Qubit States without Concurrence and Three-Tangle 2006 Robert Lohmayer
Andreas Osterloh
Jens Siewert
Armin Uhlmann
+ PDF Chat Multipartite entanglement vs nonlocality for two families of $N$-qubit states 2024 Sanchit Srivastava
Shohini Ghose
+ PDF Chat Maximally Entangled Set of Multipartite Quantum States 2013 Julio I. de Vicente
Cornelia Spee
Barbara Kraus
+ PDF Chat Complementarity between tripartite quantum correlation and bipartite Bell-inequality violation in three-qubit states 2016 Palash Pandya
Avijit Misra
Indranil Chakrabarty
+ Entanglement Universality of TGX States in Qubit-Qutrit Systems 2022 Samuel R. Hedemann
+ PDF Chat Localized quadripartite entanglement 2012 Shao-xiong Wu
Chang‐shui Yu
+ Existence criterion of genuine tripartite entanglement (6 pages) 2006 Chang‐shui Yu
He-Shan Song
+ PDF Chat Optimal entanglement generation in GHZ-type states 2023 Natalia Giovenale
L Hernandez-Martinez
Ana P. Majtey
Andrea Valdés-Hernández