# Local Transformations of Multiple Multipartite States

### Submission summary

 As Contributors: David Kenworthy Gunn · Antoine Neven Arxiv Link: https://arxiv.org/abs/2007.06256v3 (pdf) Date submitted: 2021-06-11 10:18 Submitted by: Gunn, David Kenworthy Submitted to: SciPost Physics Academic field: Physics Specialties: Quantum Physics Approach: Theoretical

### Abstract

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 Communication (LOCC) allows one to quantitatively analyse entanglement, as it induces a partial order in the Hilbert space. However, it has been shown that, for systems with fixed local dimensions, this order is generically trivial, which prevents relating multipartite states to each other with respect to any entanglement measure. In order to obtain a non-trivial partial ordering, we study a physically motivated extension of LOCC: multi-state LOCC. Here, one considers simultaneous LOCC transformations acting on a finite number of entangled pure states. We study both multipartite and bipartite multi-state transformations. In the multipartite case, we demonstrate that one can change the stochastic LOCC (SLOCC) class of the individual initial states by only applying Local Unitaries (LUs). We show that, by transferring entanglement from one state to the other, one can perform state conversions not possible in the single copy case; provide examples of multipartite entanglement catalysis; and demonstrate improved probabilistic protocols. In the bipartite case, we identify numerous non-trivial LU transformations and show that the source entanglement is not additive. These results demonstrate that multi-state LOCC has a much richer landscape than single-state LOCC.

###### Current status:
Editor-in-charge assigned

### List of changes

- Some typographical errors have been corrected.
- Some figures have been edited to make them more understandable.
- The conclusion was restructured and modified to present a broader outlook for multi-state LOCC.

### Submission & Refereeing History

Resubmission 2007.06256v3 on 11 June 2021
Resubmission 2007.06256v2 on 15 February 2021
Submission 2007.06256v1 on 24 September 2020