Abstract In many quantum information processing protocols, entangled states shared among parties are an important resource. In this article, we study how bipartite states may be distributed in the context of a quantum network limited by timing constraints. We explore various tasks that plausibly arise in this context, and characterize the achievability of several of these in settings where only one-way communication is allowed. We provide partial results in the case where two-way communication is allowed. This builds on earlier work on summoning single and bipartite systems.
Abstract In many quantum information processing protocols, entangled states shared among parties are an important resource. In this article, we study how bipartite states may be distributed in the context of a quantum network limited by timing constraints. We explore various tasks that plausibly arise in this context, and characterize the achievability of several of these in settings where only one-way communication is allowed. We provide partial results in the case where two-way communication is allowed. This builds on earlier work on summoning single and bipartite systems.
In an entanglement summoning task, a set of distributed, co-operating parties attempt to fulfill requests to prepare entanglement between distant locations. The parties share limited communication resources: timing constraints may require the entangled state be prepared before some pairs of distant parties can communicate, and a restricted set of links in a quantum network may further constrain communication. Building on earlier work, we continue the characterization of entanglement summoning. We give an if and only if condition on entanglement summoning tasks with only bidirected causal connections, and provide a set of sufficient conditions addressing the most general case containing both oriented and bidirected causal connections. Our results rely on the recent development of entanglement sharing schemes.
Quantum entanglement and coherence are two fundamental resources for quantum information processing. Recent results clearly demonstrate their relevance in quantum technological tasks, including quantum communication and quantum algorithms. In this Letter we study the role of quantum coherence for quantum state redistribution, a fundamental task where two parties aim to relocate a quantum particle by using a limited amount of quantum communication and shared entanglement. We provide general bounds for the resource rates required for this process, and show that these bounds are tight under additional reasonable constraints, including the situation where the receiving party cannot use local coherence. While entanglement cannot be directly converted into local coherence in our setting, we show that entanglement is still useful for local coherence creation if an additional quantum channel is provided, and the optimal protocol for local coherence creation for any given amount of quantum communication and shared entanglement is presented. We also discuss possible extensions of our methods to other scenarios where the receiving party is limited by local constraints, including theories of thermodynamics and asymmetry.
The phenomenon of quantum entanglement is a fundamental feature of quantum mechanics which, as a counterintuitive and inherently ”quantum” phenomenon (with no classical analogue) has been the subject of much study, especially in quantum information theory. One fruitful approach to the description of entanglement has been in its operational description - that is, in the consideration of what can be achieved using entangled states under certain restrictions, typically the regime of local operations and classical communications.\n\nWe present results here related to the operational characterisation of entanglement in the resource model, in both bipartite and multipartite cases. First, we consider the conversion between pure bipartite entangled states in terms of an often-ignored resource - the classical communication cost. Using prior results for more specific conversions, we derive lower bounds on this cost (and the related quantity of the conversion inefficiency) for general bipartite pure states.\n\nWe also consider pure-state conversions of multipartite entanglement, in particular the class of protocols in which multipartite states are converted to states shared between fewer parties. We have found a previously-unconsidered variety of such conversions, in which the target state of the conversion is a state shared between a random subset of the parties. We find that when such post-selection of parties in the protocol is permitted allows for a wider variety of achievable target states; certain states which can not be reliably obtained between predetermined parties (even some where the probability of doing so is arbitrarily small) can be obtained between random parties. We consider a variety of states in which this phenomenon occurs, as well as bounds on such protocols can achieve.\n\nFinally we consider a practical use of entanglement as a resource, in an experimental implementation of a multipartite QKD protocol. This is based on the tripartite GHZ entangled state, but can be implemented using only bipartite entanglement. We adapt existing QKD results for both the bipartite and multipartite case to derive a secure key rate for this implementation, taking into account the ways in which it differs from the idealised theoretical case.
Quantum networks connect systems at separate locations via quantum links, enabling a wide range of quantum information tasks between distant parties. Large-scale networks have the potential to enable global secure communication, distributed quantum computation, enhanced clock synchronization, and high-precision multiparameter metrology. For the optimal development of these technologies, however, it is essential to identify the necessary resources and sub-routines that will lead to the quantum advantage, but this is demanding even for the simplest protocols in quantum information processing. Here we show that quantum networks relying on the long-distance distribution of bipartite entanglement, combined with local operations and shared randomness, cannot achieve a relevant quantum advantage. Specifically, we prove that these networks do not help in preparing resourceful quantum states such as Greenberger-Horne-Zeilinger states or cluster states, despite the free availability of long-distance entanglement. At an abstract level, our work points towards a fundamental difference between bipartite and multipartite entanglement. From a practical perspective, our results highlight the need for classical communication combined with quantum memories to fully harness the power of quantum networks.
Abstract The ability to distribute entanglement over complex quantum networks is an important step towards a quantum internet. Recently, there has been significant theoretical effort, mainly focusing on the distribution of bipartite entanglement via a simple quantum network composed only of bipartite quantum channels. There are, however, a number of quantum information processing protocols based on multipartite rather than bipartite entanglement. Whereas multipartite entanglement can be distributed by means of a network of such bipartite channels, a more natural way is to use a more general network, that is, a quantum broadcast network including quantum broadcast channels. In this work, we present a general framework for deriving upper bounds on the rates at which GHZ states or multipartite private states can be distributed among a number of different parties over an arbitrary quantum broadcast network. Our upper bounds are written in terms of the multipartite squashed entanglement, corresponding to a generalisation of recently derived bounds (Azuma et al , (2016), Nat. Commun. 7 13523). We also discuss how lower bounds can be obtained by combining a generalisation of an aggregated quantum repeater protocol with graph theoretic concepts.
We consider communication between two parties using a bipartite quantum operation, which constitutes the most general quantum mechanical model of two-party communication. We primarily focus on the simultaneous forward and backward communication of classical messages. For the case in which the two parties share unlimited prior entanglement, we give inner and outer bounds on the achievable rate region that generalize classical results due to Shannon. In particular, using a protocol of Bennett, Harrow, Leung, and Smolin, we give a one-shot expression in terms of the Holevo information for the entanglement-assisted one-way capacity of a two-way quantum channel. As applications, we rederive two known additivity results for one-way channel capacities: the entanglement-assisted capacity of a general one-way channel, and the unassisted capacity of an entanglement-breaking one-way channel.