Entanglement classes of permutation-symmetric qudit states: symmetric operations suffice

Abstract

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 classical communication (SLOCC equivalence). In both cases, we show that the search can be restricted to operations where the same local operation acts on all qudits, and we provide an explicit construction for it. Stabilizers of states in the form of one-particle operations preserving permutation symmetry are shown to provide a coarse-grained classification of entanglement classes. We prove that the Jordan form of such one-particle operator is a SLOCC invariant. We find, as representatives of those classes, a discrete set of entangled states that generalize the GHZ and W state for the many-particle qudit case. In the later case, we introduce "excitation states" as a natural generalization of the W state for d>2.

8 pages; minor changes + added reference

References in corpus (6)

• Entanglement detection
• The maximally entangled symmetric state in terms of the geometric measure
• Inductive classification of multipartite entanglement under SLOCC
• The Computational Complexity of Linear Optics
• Determining the whole pure symmetric N-qubit state from its parts
• Local unitary group stabilizers and entanglement for multiqubit symmetric states

Cited by in corpus (16)

• Transformations among Pure Multipartite Entangled States via Local Operations Are Almost Never Possible
• Which multiphoton states are related via linear optics?
• Quantum scars in spin-1/2 isotropic Heisenberg clusters
• Frequency combs with parity-protected cross-correlations from dynamically modulated qubit arrays
• Matrix Product States: Entanglement, symmetries, and state transformations
• A brief introduction to multipartite entanglement
• State transformations within entanglement classes containing permutation-symmetric states
• A link between symmetries of critical states and the structure of SLOCC classes in multipartite systems
• Local unitary symmetries and entanglement invariants
• Symmetries and local transformations of translationally invariant Matrix Product States
• A solvable model for graph state decoherence dynamics
• Quantum fidelity of symmetric multipartite states
• Identifying families of multipartite states with non-trivial local entanglement transformations
• Quantum Games and Interactive Tools for Quantum Technologies Outreach and Education
• Visualizing quantum mechanics in an interactive simulation -- Virtual Lab by Quantum Flytrap
• Entanglement detection with scrambled data