# Local Transformations of Multiple Multipartite States

### Submission summary

 As Contributors: David Kenworthy Gunn · Antoine Neven Arxiv Link: https://arxiv.org/abs/2007.06256v2 (pdf) Date submitted: 2021-02-15 17:46 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

- The introduction was modified in response to the referee’s comments about the reason for studying pure state transformations. Additionally, we made small changes to make the text more readable and precise.
- In Section V, we corrected the typo in Fig.3 and added a sentence discussing permutations of Schmidt coefficients, providing a reference (Ref. [57]) to related work and an upper bound on the number of possible permutations (Eq. 57).
- We modified the conclusion to clarify the outlook of our work as suggested by the referee.
- We updated the Acknowledgements to include Ref.[55].

### Submission & Refereeing History

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

## Reports on this Submission

### Report

In the revised version, the authors made the motivation of the work more clear. Also, they improved several points mentioned in my previous report. Therefore, I recommend publication of this article.

• validity: top
• significance: good
• originality: high
• clarity: top
• formatting: excellent
• grammar: excellent