Distinguishing universality classes of two entanglement percolation protocols

Sean Fayfar, Alex Bretaña, Wouter Montfrooij +1 more

Shashaank Khanna, Ujjwal Sen, Sarika Jalan

S. Broadfoot, U. Dorner, Dieter Jaksch

We develop a concept of entanglement percolation for long-distance singlet generation in quantum networks with neighboring nodes connected by partially entangled bipartite mixed states. We give a necessary and sufficient condition on the class of mixed network states for the generation of singlets. States beyond this class are insufficient for entanglement percolation. We find that neighboring nodes are required to be connected by multiple partially entangled states and devise a rich variety of distillation protocols for the conversion of these states into singlets. These distillation protocols are suitable for a variety of network geometries and have a sufficiently high success probability even for significantly impure states. In addition to this, we discuss possible further improvements achievable by using quantum strategies including generalized forms of entanglement swapping.

Deep Nath, Soumen Roy

A quantum network is a network of entangled states, which can be used to transmit quantum information. Nonmaximally entangled states are not really effective in establishing quantum communication across vast distances. Creating and maintaining a maximally entangled state over which quantum information can be transferred more effectively is difficult in experiments, as nonmaximally entangled states are typically produced there. Therefore, we usually construct a network of nonmaximally entangled states and use the underlying network structure to establish maximal entanglement between distant nodes. Various protocols leveraging interesting aspects of quantum and statistical physics are designed to achieve long-range maximally entangled states. Here, we consider two-dimensional lattices as quantum networks where edges represent nonmaximally entangled pure states. We introduce a general protocol based on bond percolation -- general concurrence percolation (GCP) -- to create a network of maximally entangled states. The associated network obtained through GCP ought to enable the achievement of long-range quantum communication. Our observations indicate that, similar to other existing protocols, GCP falls within the percolation universality class, as determined through finite-size scaling analysis performed on two-dimensional lattices. We find that the associated percolation threshold value is smaller than that of the existing protocols. We introduce and analytically solve a minimal model that renders insight into the origin of the fundamentally lower percolation threshold achieved by GCP.

Alessandro Romancino, Jordi Romero-Pallejà, G. Massimo Palma +1 more

Entanglement percolation aims at generating maximal entanglement between any two nodes of a quantum network by utilizing strategies based solely on local operations and classical communication between the nodes. As it happens in classical percolation theory, the topology of the network is crucial, but also the entanglement shared between the nodes of the network. In a network of identically partially entangled states, the network topology determines the minimum entanglement needed for percolation. In this work, we generalize the protocol to scenarios where the initial entanglement shared between any two nodes of the network is not the same but has some randomness. In such cases, we find that for classical entanglement percolation, only the average initial entanglement is relevant. In contrast, the quantum entanglement percolation protocol (within the q-swap framework) degrades under these more realistic conditions as the width of the distribution increases, suggesting that Random CEP may become the optimal LOCC strategy in sufficiently heterogeneous quantum networks.