A link between symmetries of critical states and the structure of SLOCC classes in multipartite systems

@article{Slowik2020ALB,
  title={A link between symmetries of critical states and the structure of SLOCC classes in multipartite systems},
  author={Oskar Slowik and Martin Hebenstreit and Barbara Kraus and Adam Sawicki},
  journal={Quantum},
  year={2020},
  volume={4},
  pages={300}
}
Central in entanglement theory is the characterization of local transformations among pure multipartite states. As a first step towards such a characterization, one needs to identify those states which can be transformed into each other via local operations with a non-vanishing probability. The classes obtained in this way are called SLOCC classes. They can be categorized into three disjoint types: the null-cone, the polystable states and strictly semistable states. Whereas the former two are… 

Figures from this paper

Designing locally maximally entangled quantum states with arbitrary local symmetries
TLDR
This work shows how to design critical states with arbitrarily large local unitary symmetry that can be realised in a quantum system of distinguishable traps with bosons or fermions occupying a finite number of modes and establishes the existence of so-called strictly semistable states with particular asymptotic diagonal symmetries.
Stochastic local operations with classical communication of absolutely maximally entangled states
Absolutely Maximally Entangled (AME) states are maximally entangled for every bipartition of the system. They are crucial resources for various quantum information protocols. We present techniques
Analysis of Neural Network Predictions for Entanglement Self-Catalysis
TLDR
This work investigates whether distinct models of neural networks can learn how to detect catalysis and self-catalysis of entanglement and also studies whether a trained machine can detect another related phenomenon which is dub transfer knowledge.
Local transformations of multiple multipartite states
Understanding multipartite entanglement is vital, as it underpins a wide range of phenomena across physics. The study of transformations of states via Local Operations assisted by Classical

References

SHOWING 1-10 OF 113 REFERENCES
Discrete And Differentiable Entanglement Transformations
The study of transformations among pure states via Local Operations assisted by Classical Communication (LOCC) plays a central role in entanglement theory. The main emphasis of these investigations
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
Necessary and sufficient conditions for local manipulation of multipartite pure quantum states
Suppose that several parties jointly possess a pure multipartite state, |?. Using local operations on their respective systems and classical communication (i.e. LOCC), it may be possible for the
Finitely correlated states on quantum spin chains
We study a construction that yields a class of translation invariant states on quantum spin chains, characterized by the property that the correlations across any bond can be modeled on a
The invariant-comb approach and its relation to the balancedness of multipartite entangled states
The invariant-comb approach is a method to construct entanglement measures for multipartite systems of qubits. The essential step is the construction of an antilinear operator that we call comb in
Convexity of momentum map, Morse index, and quantum entanglement
We analyze from the topological perspective the space of all SLOCC (Stochastic Local Operations with Classical Communication) classes of pure states for composite quantum systems. We do it for both
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
Transformations among Pure Multipartite Entangled States via Local Operations are Almost Never Possible
Local operations assisted by classical communication (LOCC) constitute the free operations in entanglement theory. Hence, the determination of LOCC transformations is crucial for the understanding of
Classification scheme of pure multipartite states based on topological phases
We investigate the connection between the concept of a-balancedness introduced in [Phys. Rev A. 85, 032112 (2012)] and polynomial local SU invariants and the appearance of topological phases
Classification of multipartite entanglement of all finite dimensionality.
We provide a systematic classification of multiparticle entanglement in terms of equivalence classes of states under stochastic local operations and classical communication (SLOCC). We show that such
...
1
2
3
4
5
...