Algebraic characterization of X-states in quantum information

Abstract

A class of two-qubit states called X-states are increasingly being used to discuss entanglement and other quantum correlations in the field of quantum information. Maximally entangled Bell states and "Werner" states are subsets of them. Apart from being so named because their density matrix looks like the letter X, there is not as yet any characterization of them. The su(2) X su(2) X u(1) subalgebra of the full su(4) algebra of two qubits is pointed out as the underlying invariance of this class of states. X-states are a seven-parameter family associated with this subalgebra of seven operators. This recognition provides a route to preparing such states and also a convenient algebraic procedure for analytically calculating their properties. At the same time, it points to other groups of seven-parameter states that, while not at first sight appearing similar, are also invariant under the same subalgebra. And it opens the way to analyzing invariant states of other subalgebras in bipartite systems.

4 pages, 1 figure

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Cited by in corpus (55)

• Quantum discord for two-qubit X-states
• Robustness of asymmetry and coherence of quantum states
• Optimal measurements to access classical correlations of two-qubit states
• Energy Cost of Creating Quantum Coherence
• Unified view of correlations using the square norm distance
• Asymmetry and coherence weight of quantum states
• Fidelity susceptibility and quantum Fisher information for density operators with arbitrary ranks
• On the quantum correlations in two-qubit XYZ spin chains with Dzyaloshinsky-Moriya and Kaplan-Shekhtman-Entin-Wohlman-Aharony interactions
• Entanglement universality of two-qubit X-states
• Quantum properties and dynamics of X states
• Entanglement Sudden Death in Three Qubit X-States
• On the quantum discord of general X states
• Quantum discord for a two-parameter class of states in $2\otimes d$ quantum systems
• Partial coherence and quantum correlation with fidelity and affinity distances
• Roadmap on Quantum Thermodynamics
• Analytical solutions and criteria for the quantum discord of two-qubit X-states
• Generalized X states of N qubits and their symmetries
• Creation of quantum correlations between two atoms in a dissipative environment from an initial vacuum state
• Magnetic Properties and Thermal Entanglement on a Triangulated Kagome Lattice
• Calculation of quantum discord in arbitrary dimensions, especially for X- and other specialized states
• Volumes of conditioned bipartite state spaces
• Sudden change in dynamics of genuine multipartite entanglement of cavity-reservoir qubits
• Quantum Correlation Dynamics in Controlled Two-Coupled-Qubit Systems
• Optimal path for a quantum teleportation protocol in entangled networks
• NMR dynamics of quantum discord for spin-carrying gas molecules in a closed nanopore
• Topology of Entanglement Evolution of Two Qubits
• Entanglement Harvesting and Quantum Discord of Alpha Vacua in de Sitter Space
• The role of phases in detecting three-qubit entanglement
• Shareability of steering in 2-producible states
• Geometric quantum discord and coherence in a dipolar interacting magnetic system
• A finite geometric toy model of space-time as an error correcting code
• Dynamic Stark effect, light emission, and entanglement generation in a laser-driven quantum optical system
• Two-qubit mixed states and teleportation fidelity: Purity, concurrence, and beyond
• Entanglement in bipartite quantum systems: Euclidean volume ratios and detectability by Bell inequalities
• $X$-States From a Finite Geometric Perspective
• On the power of one pure steered state for EPR-steering with a pair of qubits
• Bounding the entanglement of N qubits with only four measurements
• Partial Transpose Moments, Principal Minors and Entanglement Detection
• Quantitative characterization of several entanglement detection criteria
• Simple permutation-based measure of quantum correlations and maximally-3-tangled states
• Relation Between Stereographic Projection and Concurrence Measure in Bipartite Pure States
• Emergence of $X$ states in a quantum impurity model
• Genuine entanglement under squeezed generalized amplitude damping channels with memory
• Controllable coupling and quantum correlation dynamics of two double quantum dots coupled via a transmission line resonator
• Local available quantum correlations of X states: The symmetric and anti-symmetric cases
• Non-maximally entangled mixed states of X and non-X types as teleportation channels
• The use of the output states generated by the broadcasting of entanglement in quantum teleportation
• Detecting Two Qubit Both-Way Positive Discord States
• Local available quantum correlations of non-symmetric X states
• Quantum Correlations in NMR systems
• Performance of entanglement purification including maximally entangled mixed states
• Chaotic spin-spin entanglement on a recursive lattice
• Entanglement in bipartite X-states: Analytical results for the volume of states with positive partial transpose
• Comparing coherence measures for X states: Can quantum states be ordered based on quantum coherence?
• Sudden change of genuine multipartite entanglement in non-Markovian dynamics