Quantum Information and Computation

Distribution of entanglement in networks of bi-partite full-rank mixed states

G John Lapeyre Jr., Sébastien Perseguers, Maciej Lewenstein, Antonio Acín

Published May 1, 2012• 5 citations

Abstract

We study quantum entanglement distribution on networks with full-rank bi-partite mixed states linking qubits on nodes. In particular, we use entanglement swapping and purification to partially entangle widely separated nodes. The simplest method consists of performing entanglement swappings along the shortest chain of links connecting the two nodes. However, we show that this method may be improved upon by choosing a protocol with a specific ordering of swappings and purifications. A priori, the design that produces optimal improvement is not clear. However, we parameterize the choices and find that the optimal values depend strongly on the desired measure of improvement. As an initial application, we apply the new improved protocols to the Erd\"os--R\'enyi network and obtain results including low density limits and an exact calculation of the average entanglement gained at the critical point.

DOI: 10.26421/qic12.5-6-10

Related papers

Distribution of entanglement in networks of bi-partite full-rank mixed states

Lapeyre, G. J., Sébastien Perseguers, Maciej Lewenstein +1 more

We study quantum entanglement distribution on networks with full-rank bi-partite mixed states linking qubits on nodes. In particular, we use entanglement swapping and purification to partially entangle widely separated nodes. The simplest method consists of performing entanglement swappings along the shortest chain of links connecting the two nodes. However, we show that this method may be improved upon by choosing a protocol with a specific ordering of swappings and purifications. A priori, the design that produces optimal improvement is not clear. However, we parametrize the choices and find that the optimal values depend strongly on the desired measure of improvement. As an initial application, we apply the new improved protocols to the Erdös--Rényi network and obtain results including low density limits and an exact calculation of the average entanglement gained at the critical point.

arXiv:1108.5833Aug 30, 20110 citations

Entanglement swapping of two arbitrarily degraded entangled states

Brian T. Kirby, Siddhartha Santra, Vladimir S. Malinovsky +1 more

We consider entanglement swapping, a key component of quantum network operations and entanglement distribution. Pure entangled states, which are the desired input to the swapping protocol, are typically mixed by environmental interactions, causing a reduction in their degree of entanglement. Thus an understanding of entanglement swapping with partially mixed states is of importance. Here we present a general analytical solution for entanglement swapping of arbitrary two-qubit states. Our result provides a comprehensive method for analyzing entanglement swapping in quantum networks. First, we show that the concurrence of a partially mixed state is conserved when this state is swapped with a Bell state. Then, we find upper and lower bounds on the concurrence of the state resulting from entanglement swapping for various classes of input states. Finally, we determine a general relationship between the ranks of the initial states and the rank of the final state after swapping.

arXiv:1512.06093Physical Review AJul 20, 201649 citations

REDiP: Ranked Entanglement Distribution Protocol for the Quantum Internet

Leonardo Bacciottini, Luciano Lenzini, Enzo Mingozzi +1 more

The distribution of entangled qubit pairs to end nodes is the key requirement of a quantum network to enable qubit state transmission through quantum teleportation. Existing protocols for entanglement distribution fix a specific swapping order on the involved quantum repeaters and delegate entanglement purification to upper-layer protocols. This limitation is problematic because entangled states tend to degrade due to quantum noise, and they cannot be purified if their fidelity (i.e. quality) falls below a certain threshold. It is therefore of the utmost importance to co-plan entanglement swapping and purification to achieve a target end-to-end fidelity. In this work, we present the Ranked Entanglement Distribution Protocol (REDiP), which overcomes the aforementioned limits by including the "ranks" mechanism to configure the ordering of both purification and entanglement swapping steps. We show how REDiP can easily be configured to implement custom entanglement swapping and purification strategies, including (but not restricted to) those adopted in two recent works. We also propose an algorithm to estimate the bandwidth to allocate on every link of the REDiP path, and we provide a set of guidelines on how REDiP ranks can be configured depending on user requirements and hardware configuration. Such guidelines are driven by original insights into purification performance. We conduct simulations to verify our results and assess the impact of different REDiP configurations on the performance of a repeater network, in terms of throughput and fidelity.

IEEE Open Journal of the Communications SocietyDec 20, 20237 citations

Optimal Fidelity-Aware Entanglement Distribution in Linear Quantum Networks

Iordanis Koutsopoulos

We study the problem of entanglement distribution in terms of maximizing a utility function that captures the total fidelity of end-to-end entanglements in a two-link linear quantum network with a source, a repeater, and a destination. The nodes have several quantum memories, and the problem is how to coordinate entanglement purification in each of the links, and entanglement swapping across links so as to achieve the goal above. We show that entanglement swapping (i.e, deciding on the pair of qubits from each link to perform swapping on) is equivalent to finding a max-weight matching on a bipartite graph. Further, entanglement purification (i.e, deciding which pairs of qubits in a link will undergo purification) is equivalent to finding a max-weight matching on a non-bipartite graph. We propose two polynomial algorithms, the Purify-then-Swap (PtS) and the Swap-then-Purify (StP) ones, where the decisions about purification and swapping are taken with different order. Numerical results show that PtS performs better than StP, and that the omission of purification in StP gives substantial benefits.

arXiv:2407.09171IEEE Military Communications Conference (MILCOM)Oct 28, 20242 citations

Singlet generation in mixed-state quantum networks

S. Broadfoot, U. Dorner, Dieter Jaksch

We study the generation of singlets in quantum networks with nodes initially sharing a finite number of partially entangled bipartite mixed states. We prove that singlets between arbitrary nodes in such networks can be created if and only if the initial states connecting the nodes have a particular form. We then generalize the method of entanglement percolation, previously developed for pure states, to mixed states of this form. As part of this, we find and compare different distillation protocols necessary to convert groups of mixed states shared between neighboring nodes of the network into singlets. In addition, we discuss protocols that only rely on local rules for the efficient connection of two remote nodes in the network via entanglement swapping. Further improvements of the success probability of singlet generation are developed by using particular forms of ``quantum preprocessing'' on the network. This includes generalized forms of entanglement swapping and we show how such strategies can be embedded in regular and hierarchical quantum networks.

arXiv:0912.3214Physical Review AApr 22, 201019 citations

Enhancing the teleportation fidelity of a quantum network using purification

Soumit Roy, Md Sohel Mondal, Siddhartha Santra +1 more

Complex quantum networks can support a diverse set of long-range entanglement distribution schemes ranging from linear repeater protocols to multipath entanglement purification strategies. As a result, a network's resourcefulness, that is its ability to facilitate quantum communication, depends on the deployed distribution scheme. In this work, we analyse and compare the resourcefulness of quantum networks across a broad range of network topologies, including both regular and random networks, under two distinct entanglement distribution schemes. The first relies on entanglement swapping along a single path connecting a source-target pair, while the second exploits entanglement purification using multiple paths between the same source and target nodes. The resourcefulness of the network is quantified using a recently described metric [1] that averages over the maximum teleportation fidelity between arbitrary source-target pairs in the network. We present algorithms for estimating this metric under constraints of edge-usage and ordering of paths. Our results not only demonstrate the sensitivity of the average maximum teleportation fidelity metric to the choice of entanglement distribution protocol, but also highlight the significant improvements enabled by network purification schemes. In particular, purification-based approaches can substantially enhance average teleportation fidelity, thereby improving the overall teleportation capability of quantum networks.

quant-pharXiv:2606.18743Jun 18, 20260 citations