The maximally entangled symmetric state in terms of the geometric measure

  title={The maximally entangled symmetric state in terms of the geometric measure},
  author={Martin Aulbach and Damian Markham and Mio Murao},
  journal={New Journal of Physics},
The geometric measure of entanglement is investigated for permutation symmetric pure states of multipartite qubit systems, in particular the question of maximum entanglement. This is done with the help of the Majorana representation, which maps an n qubit symmetric state to n points on the unit sphere. It is shown how symmetries of the point distribution can be exploited to simplify the calculation of entanglement and also help find the maximally entangled symmetric state. Using a combination… 
Entanglement in the symmetric sector of n qubits.
The manifold of maximally entangled 3 qubit state, both in the symmetric and generic case, is analyzed and a cross ratio of related Möbius transformations are shown to play a central role.
Quantum states that are symmetric with respect to permutations of their subsystems appear in a wide range of physical settings, and they have a variety of promising applications in quantum
All possible permutational symmetries of a quantum system
We investigate the intermediate permutational symmetries of a system of qubits, that lie in between the perfect symmetric and antisymmetric cases. We prove that, on average, pure states of qubits
Entanglement and symmetry in permutation-symmetric states
We investigate the relationship between multipartite entanglement and symmetry, focusing on permutation symmetric states. We give a highly intuitive geometric interpretation to entanglement via the
Entanglement classes of symmetric Werner states
An understanding of structure and entanglement properties of mixed Werner states is known for bipartite and tripartite systems of arbitrary dimension [2, 23], but remains an open problem for higher
State transformations within entanglement classes containing permutation-symmetric states
The study of state transformations under local operations and classical communication (LOCC) plays a crucial role in entanglement theory. While this has been long ago characterized for pure bipartite
Local Unitary Equivalent Classes of Symmetric N-Qubit Mixed States
Majorana representation (MR) of symmetric N-qubit pure states has been used successfully in entanglement classification. Generalization of this has been a long standing open problem due to the
Entanglement entropy in quasi-symmetric multi-qubit states
We generalize the symmetric multi-qubit states to their q-analogs, whose basis vectors are identified with the q-Dicke states. We study the entanglement entropy in these states and find that
Entanglement classes of permutation-symmetric qudit states: Symmetric operations suffice
We analyse entanglement classes for permutation-symmetric states for n qudits (i.e. d-level systems), with respect to local unitary operations (LU-equivalence) and stochastic local operations and
Entanglement in highly symmetric multipartite quantum states
We present a construction of genuinely entangled multipartite quantum states based on the group theory. Analyzed states resemble the Dicke states, whereas the interactions occur only between specific


Geometric measure of entanglement for symmetric states
Is the closest product state to a symmetric entangled multiparticle state also symmetric? This question has appeared in the recent literature concerning the geometric measure of entanglement. First,
Geometric measure of entanglement and applications to bipartite and multipartite quantum states
The degree to which a pure quantum state is entangled can be characterized by the distance or angle to the nearest unentangled state. This geometric measure of entanglement, already present in a
Maximally entangled three-qubit states via geometric measure of entanglement
Bipartite maximally entangled states have the property that the largest Schmidt coefficient reaches its lower bound. However, for multipartite states, the standard Schmidt decomposition generally
Robustness of entanglement
In the quest to completely describe entanglement in the general case of a finite number of parties sharing a physical system of finite-dimensional Hilbert space an entanglement magnitude is
Three qubits can be entangled in two inequivalent ways
Invertible local transformations of a multipartite system are used to define equivalence classes in the set of entangled states. This classification concerns the entanglement properties of a single
Reduced state uniquely defines the Groverian measure of the original pure state
Groverian and Geometric entanglement measures of the n-party pure state are expressed by the (n-1)-party reduced state density operator directly. This main theorem derives several important
Characterizing the entanglement of symmetric many-particle spin-1/2 systems
Analyzing the properties of entanglement in many-particle spin-1/2 systems is generally difficult because the system's Hilbert space grows exponentially with the number of constituent particles, N.
Operational families of entanglement classes for symmetric N-qubit States.
We solve the entanglement classification under stochastic local operations and classical communication (SLOCC) for all multipartite symmetric states in the general N-qubit case. For this purpose, we
Entanglement equivalence of N-qubit symmetric states
We study the interconversion of multipartite symmetric N-qubit states under stochastic local operations and classical communication (SLOCC). We demonstrate that if two symmetric states can be
Entanglement and local information access for graph states
It is shown that for a class of graph states, including d-dimensional cluster states, the Greenberger–Horne–Zeilinger states, and some related mixed states, a number of multipartite entanglement measures give an operational interpretation as the maximal number of graphStates distinguishable by local operations and classical communication (LOCC), as well as supplying a tight bound on the fixed letter classical capacity under LOCC decoding.