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arXiv:quant-ph/0410016 · Physical Review Letters

Remote Preparation and Distribution of Bipartite Entangled States

Gilad Gour, Barry C. Sanders

Published Dec 20, 2004• 61 citations
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Abstract

We prove a powerful theorem for tripartite remote entanglement distribution protocols that establishes an upper bound on the amount of entanglement of formation that can be created between two single-qubit nodes of a quantum network. Our theorem also provides an operational interpretation of concurrence as a type of entanglement capacity.

DOI
10.1103/physrevlett.93.260501

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We prove a powerful theorem for tripartite remote entanglement distribution protocols that establishes an upper bound on the amount of entanglement of formation that can be created between two single-qubit nodes of a quantum network. Our theorem also provides an operational interpretation of concurrence as a type of entanglement capacity.
We present a powerful theorem for tripartite remote entanglement distribution protocols, which provides an operational interpretation of concurrence as a type of entanglement capacity, and we establish that concurrence of assistance, which we show is an entanglement monotone, identifies capabilities of and limitations to producing pure bipartite entangled states from pure tripartite entangled states. In addition, we show that, if concurrence of assistance for the pure tripartite state is at least as large as the concurrence of the desired pure bipartite state, then the former may be transformed to the latter via local operations and classical communication, and we calculate the maximum probability for this transformation when this condition is not met.PACS Nos.: 03.67.Mn, 03.67.Hk, 03.65.Ud
We extend the definition of concurrence into a family of entanglement monotones, which we call concurrence monotones. We discuss their properties and advantages as computational manageable measures of entanglement, and show that for pure bipartite states all measures of entanglement can be written as functions of the concurrence monotones. We then show that the concurrence monotones provide bounds on quantum information tasks. As an example, we discuss their applications to remote entanglement distributions (RED) such as entanglement swapping and remote preparation of bipartite entangled states (RPBES). We prove a powerful theorem which states what kind of (possibly mixed) bipartite states or distributions of bipartite states cannot be remotely prepared. The theorem establishes an upper bound on the amount of GGG-concurrence (one member in the concurrence family) that can be created between two single-qudit nodes of quantum networks by means of tripartite RED. For pure bipartite states the bound on the GGG-concurrence can always be saturated by RPBES.
Using the convex-roof extended negativity and the negativity of assistance as quantifications of bipartite entanglement, we consider the possible remotely-distributed entanglement. For two pure states ∣ϕ⟩AB\ketϕ_{AB}∣ϕ⟩AB​ and ∣ψ⟩CD\ketψ_{CD}∣ψ⟩CD​ on bipartite systems ABABAB and CDCDCD, we first show that the possible amount of entanglement remotely distributed on the system ACACAC by joint measurement on the system BDBDBD is not less than the product of two amounts of entanglement for the states ∣ϕ⟩AB\ketϕ_{AB}∣ϕ⟩AB​ and ∣ψ⟩CD\ketψ_{CD}∣ψ⟩CD​ in two-qubit and two-qutrit systems. We also provide some sufficient conditions, for which the result can be generalized into higher-dimensional quantum systems.
Scaling the number of entangled nodes in a quantum network is a challenge with significant implications for quantum computing, clock synchronisation, secure communications, and quantum sensing. In a quantum network, photons interact with matter qubits at different nodes, flexibly enabling the creation of remote entanglement between them. Multipartite entanglement among multiple nodes will be crucial for many proposed quantum network applications, including quantum computational tasks and quantum metrology. To date, experimental efforts have primarily focused on generating bipartite entanglement between nodes, which is widely regarded as the fundamental quantum resource for quantum networks. However, relying exclusively on bipartite entanglement to form more complex multipartite entanglement introduces several challenges. These include the need for ancillary qubits, extensive local entangling operations which increases the preparation latency, and increasingly stringent requirements on coherence times as the number of nodes grows. Here, we analyse various schemes that achieve multipartite entanglement between nodes in a single step, bypassing the need for multiple rounds of bipartite entanglement. We demonstrate that different schemes can produce distinct multipartite entangled states, with varying fidelity and generation rates. Additionally, we discuss the applicability of these schemes across different experimental platforms, highlighting their primary advantages and disadvantages.