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Protocols to share genuine multipartite entanglement employing copies of biseparable states

Swati Choudhary, Ujjwal Sen, Saronath Halder

TL;DR

The paper tackles activating genuine multipartite entanglement (GME) from copies of biseparable states, without relying on joint measurements. It introduces a two-copy protocol for $3$-level systems ($3$-qutrits) and generalizes to arbitrary numbers of parties, also showing activation of genuine nonlocality alongside GME. The core mechanism distills bipartite entanglement from biseparable copies via LOCC and then fuses these resources into a pure GME state, with a distillation-free variant proposed to reduce copy requirements. The work extends to higher dimensions with $3$-qudit and beyond, analyzes success probabilities in a scalable class of states, and demonstrates that sequential single-copy access can realize robust GME activation with practical advantages for quantum networks.

Abstract

Sharing genuine multipartite entanglement by considering collective use of copies of biseparable states, which are entangled across all bipartitions but lack genuine multipartite entanglement at the single-copy level, plays a central role in several quantum information processing protocols, and has been referred as genuine multipartite entanglement activation. We present a protocol for three-qutrit systems showing that two copies of rank-two biseparable states, entangled across every bipartition, are sufficient to generate a genuinely multipartite entangled state with nonzero probability. This contrasts with the three-qubit scenario where many copies of biseparable states might be required for sharing genuine multipartite entanglement. We subsequently generalize our protocols to the case of an arbitrary number of parties. Our protocol does not rely on the implementation of joint measurements on the copies of states. Interestingly, the proposed construction naturally leads to the activation of genuinely nonlocal correlations, yielding a result that is stronger than genuine multipartite entanglement activation alone.

Protocols to share genuine multipartite entanglement employing copies of biseparable states

TL;DR

The paper tackles activating genuine multipartite entanglement (GME) from copies of biseparable states, without relying on joint measurements. It introduces a two-copy protocol for -level systems (-qutrits) and generalizes to arbitrary numbers of parties, also showing activation of genuine nonlocality alongside GME. The core mechanism distills bipartite entanglement from biseparable copies via LOCC and then fuses these resources into a pure GME state, with a distillation-free variant proposed to reduce copy requirements. The work extends to higher dimensions with -qudit and beyond, analyzes success probabilities in a scalable class of states, and demonstrates that sequential single-copy access can realize robust GME activation with practical advantages for quantum networks.

Abstract

Sharing genuine multipartite entanglement by considering collective use of copies of biseparable states, which are entangled across all bipartitions but lack genuine multipartite entanglement at the single-copy level, plays a central role in several quantum information processing protocols, and has been referred as genuine multipartite entanglement activation. We present a protocol for three-qutrit systems showing that two copies of rank-two biseparable states, entangled across every bipartition, are sufficient to generate a genuinely multipartite entangled state with nonzero probability. This contrasts with the three-qubit scenario where many copies of biseparable states might be required for sharing genuine multipartite entanglement. We subsequently generalize our protocols to the case of an arbitrary number of parties. Our protocol does not rely on the implementation of joint measurements on the copies of states. Interestingly, the proposed construction naturally leads to the activation of genuinely nonlocal correlations, yielding a result that is stronger than genuine multipartite entanglement activation alone.
Paper Structure (7 sections, 3 theorems, 12 equations)

This paper contains 7 sections, 3 theorems, 12 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Results
  4. Higher dimensional states for GME activation
  5. Success probability for a large number of copies
  6. Generalization
  7. Conclusion

Key Result

Proposition 1

Any three-qubit rank-2 biseparable state that is entangled across every bipartition, is useful for genuine multipartite entanglement (GME) activation.

Theorems & Definitions (11)

  • Definition 1
  • Definition 2
  • Definition 3
  • Definition 4
  • Proposition 1
  • proof
  • Remark 1
  • Proposition 2
  • proof
  • Proposition 3
  • ...and 1 more