Rates of multi-partite entanglement transformations and applications in quantum networks

Abstract

The theory of the asymptotic manipulation of pure bipartite quantum systems can be considered completely understood: The rates at which bipartite entangled states can be asymptotically transformed into each other are fully determined by a single number each, the respective entanglement entropy. In the multi-partite setting, similar questions of the optimally achievable rates of transforming one pure state into another are notoriously open. This seems particularly unfortunate in the light of the revived interest in such questions due to the perspective of experimentally realizing multi-partite quantum networks. In this work, we report substantial progress by deriving surprisingly simple upper and lower bounds on the rates that can be achieved in asymptotic multi-partite entanglement transformations. These bounds are based on ideas of entanglement combing and state merging. We identify cases where the bounds coincide and hence provide the exact rates. As an example, we bound rates at which resource states for the cryptographic scheme of quantum secret sharing can be distilled from arbitrary pure tripartite quantum states, providing further scope for quantum internet applications beyond point-to-point.

4+7 pages, 1 figure, v2 is significantly extended in its results and presents a general statement providing bounds for achievable asymptotic rates for an arbitrary number of parties

References in corpus (9)

• The Quantum Internet
• Description of quantum coherence in thermodynamic processes requires constraints beyond free energy
• Quantum information can be negative
• Entanglement of assistance and multipartite state distillation
• Quantum network routing and local complementation
• Shortcuts to quantum network routing
• Entanglement manipulation of multipartite pure states with finite rounds of classical communication
• Transforming graph states using single-qubit operations
• Multi-partite entanglement

Cited by in corpus (10)

• Universal Limitations on Quantum Key Distribution over a Network
• Catalytic Transformations of Pure Entangled States
• Catalysis of entanglement and other quantum resources
• Catalytic and asymptotic equivalence for quantum entanglement
• New Protocols for Conference Key and Multipartite Entanglement Distillation
• Metrology-assisted entanglement distribution in noisy quantum networks
• Device-Independent Certification of Multipartite Distillable Entanglement
• Squashed quantum non-Markovianity: a measure of genuine quantum non-Markovianity in states
• Multipartite entanglement theory with entanglement-nonincreasing operations
• Statistics of Entanglement Transformation with Hierarchies among Catalysts