Generalized X states of N qubits and their symmetries

Abstract

Several families of states such as Werner states, Bell-diagonal states and Dicke states are useful to understand multipartite entanglement. Here we present a [2^(N+1)-1]-parameter family of N-qubit "X states" that embrace all those families, generalizing previously defined states for two qubits. We also present the algebra of the operators that characterize the states and an iterative construction for this algebra, a sub-algebra of su(2^(N)). We show how a variety of entanglement witnesses can detect entanglement in such states. Connections are also made to structures in projective geometry.

arXiv comment4 pages, 2 figures

References in corpus (22)

• Introducing Quantum Discord
• Three qubits can be entangled in two inequivalent ways
• Quantum secret sharing
• Entanglement detection
• Classical, quantum and total correlations
• Finite-Time Disentanglement via Spontaneous Emission
• A Class of Quantum Error-Correcting Codes Saturating the Quantum Hamming Bound
• Sudden Death of Entanglement
• On the Power of One Bit of Quantum Information
• Experimental quantum computing without entanglement
• Quantum discord for two-qubit X-states
• Four qubits can be entangled in nine different ways
• Classification of mixed three-qubit states
• Classical Correlation and Quantum Discord in Critical Systems
• Classical and quantum correlations under decoherence
• Subsystem Purity as an Enforcer of Entanglement
• Algebraic characterization of X-states in quantum information
• The geometry of entanglement: metrics, connections and the geometric phase
• Hastening, delaying, or averting sudden death of quantum entanglement
• Experimental approximation of the Jones polynomial with DQC1
• Projective Ring Line Encompassing Two-Qubits
• Robust and Fragile Entanglement of Three Qubits: Relation to Permutation Symmetry

Cited by in corpus (13)

• Robustness of coherence: An operational and observable measure of quantum coherence
• Calculation of quantum discord for qubit-qudit or N qubits
• Asymmetry and coherence weight of quantum states
• Calculation of quantum discord in arbitrary dimensions, especially for X- and other specialized states
• Construction of multi-qubit optimal genuine entanglement witnesses
• Three-qubit entanglement witnesses with the full spanning properties
• Revealing Quantum Advantage in a Quantum Network
• Inertias of entanglement witnesses
• The role of phases in detecting three-qubit entanglement
• Separability criterion for three-qubit states with a four dimensional norm
• $X$-States From a Finite Geometric Perspective
• Bounding the entanglement of N qubits with only four measurements
• Separability of multi-qubit states in terms of diagonal and anti-diagonal entries