Entanglement purification with two entangled resource pairs is widely employed in the literature on quantum repeater networks to counteract fidelity degradation introduced by noisy quantum memories and entanglement swapping across multiple hops. Standard purification protocols assume both resource pairs carry identical fidelity. In practice, entanglement generation is stochastic, the two resource pairs are heralded at different times, and so the first pair decoheres in memory while the second is being generated. Thus a fidelity asymmetry is a structural feature of any network operating under realistic memory conditions, leading to the question: when is it beneficial to perform purification? We derive a closed-form fidelity asymmetry tolerance delta(F) that governs whether a purification attempt is beneficial. We determine a universal upper bound delta_max of approximately 0.076 beyond which purification is always counterproductive. Our simulations show that with exponential memory decoherence, purification yields benefits in only approximately 14% of purification attempts on two resource pairs in a two-hop repeater chain. We define three network objectives: fidelity only, time only, and a combination of time and fidelity, to deliver end-to-end entanglement. We show that when the application fidelity requirement is achievable through swapping alone, no-purification is the superior policy, with its advantage increasing with the number of hops. When the fidelity requirement cannot be met with swapping alone and purification is necessary, to be effective, it must be conditioned on delta(F) between resource pairs. We introduce DeltaPurify, a policy that conditions purification decisions on local fidelity information, and show it reduces time-to-serve relative to both naive purification and no-purification across several fidelity thresholds and hops of a repeater chain.
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.
Quantum data-center networks must distribute entanglement between QPUs over paths whose length grows with system scale, but each entanglement-swapping step reduces the quality of the raw end-to-end state. Topology, multiplexing, and repeated connection attempts can increase the number of raw end-to-end copies available for a request, yet they do not answer the central resource question: whether those copies are sufficient to remove, via entanglement purification, the fidelity loss caused by multi-hop distribution. We study this question through a topology-independent black-box model of the network. Each elementary link is modeled as a Werner state with parameter
w0, so ideal swapping over an
ℓ-link path produces equal-quality raw copies with Werner parameter
w0ℓ; purification succeeds if it outputs at least one state with Werner parameter at least
w0 with probability at least
pth. We compare recursive BBPSSW purification with higher-order
r-to-
1 bilocal-Clifford purification protocols of Jansen \emph{et al.}, using an all-in recursive schedule whose success probability is computed by exact dynamic programming. The resulting resource landscapes show a threshold structure governed by the Werner entanglement condition
w0ℓ>1/3 and demonstrate that multi-copy purification substantially improves both feasibility and copy efficiency. Across the evaluated grid, the Jansen family requires fewer copies than BBPSSW at more than
96% of shared feasible points; at
pth=0.70, the median copy budget drops from
268 to
30. These results provide a quantitative purification-resource benchmark for assessing whether future quantum data-center architectures can practically support hop-independent end-to-end entanglement quality.
End-to-end entanglement distribution in multi-hop quantum networks experiences fidelity degradation as entanglement swapping progresses over noisy and heterogeneous channels. In this paper, we propose a virtual-link purification strategy in which multiple EPR pairs are used at each stage to create virtual links between non-adjacent nodes and then purified in cascade using symmetric purification. The approach allows parameterizing the number of links per stage and follows a hierarchical design, with a more complete first stage and simplified purification in subsequent stages. We implement a time-slot-based orchestrator and compare the proposal against conventional swapping under Werner and bit-flip noise models. The results indicate higher end-to-end fidelity with virtual-link purification.
Generating high fidelity link-level entanglements is essential for the distribution of end-to-end connectivity across quantum communication networks. The efficiency of entanglement buffering is, however, limited by the short lifetime of the required qubits as noise causes a rapid decay in their fidelities. Entanglement purification, which is essentially a probabilistic operation, counteracts this decay. In its simplest form it uses two entanglements to obtain a higher fidelity one. In this paper, we combine entanglement buffering and purification by applying a purification protocol that acts on the stored entanglements beyond their generation time. Considering a link-level system with a few quantum memories to buffer entanglements in addition to application requests for entanglement, we use a Markov Chain model to derive the steady state distribution of the service performance metrics, specifically, (i) the fidelity of the entanglements that are consumed by application requests and (ii) the distribution of their waiting time in the request queue. Our evaluations show a trade-off between the fidelity and the request waiting time, specifically, given purification as well as for different memory sizes.
Recently emerged as a disruptive networking paradigm, quantum networks rely on the mysterious quantum entanglement to teleport qubits without physically transferring quantum particles. However, the state of quantum systems is extremely fragile due to environment noise. A promising technique to combat against quantum decoherence is entanglement purification. To fully exploit its benefit, two fundamental research questions need to be answered: (1) given an entanglement path, what is the optimal entanglement purification schedule? (2) how to compute min-cost end-to-end entanglement paths subject to fidelity constraint? In this paper, we give algorithmic solutions to both questions. For the first question, we develop an optimal entanglement purification scheduling algorithm for the single-hop case and analyze the \textsc{purify-and-swap} strategy in the multi-hop case by establishing the closed-form condition for its optimality. For the second question, we design a polynomial-time algorithm constructing an
ε-optimal fidelity-constrained path. The effectiveness of our algorithms are also numerically demonstrated by extensive simulations.
Entanglement routing establishes entangled pairs between distant nodes of a quantum network by purifying and swapping pairs generated on elementary links. Existing methods typically restrict the decision space along two axes: the operation order, often fixed to purify-then-swap (PtS), and the purification schedule of each link, often restricted to pumping. Focusing on linear repeater chains with finite link capacities, we relax both restrictions and study the maximization of the expected end-to-end throughput subject to a fidelity threshold under two quantum-noise models. We develop a unified capacity-aware optimization framework comprising an exact mixed-integer linear program (MILP) under PtS, instantiated with either pumping or general tree purification schedules, and an exact dynamic program (DP) over arbitrary operation orders. Under symmetric Pauli noise, we prove that pumping converges to a fidelity strictly below unity, imposing a capacity-independent feasibility bound and a maximum chain length on every pumping-based PtS method, whereas general tree schedules yield a capacity-dependent bound. We further prove that post-swap purification never increases the throughput, so a free operation order can only increase feasibility. Numerical evaluations confirm the bounds: tree schedules serve over 90\% of the requests that pumping cannot at moderate fidelity thresholds; within the pumping class, a free operation order recovers much of this advantage; but once links use tree schedules, the tree-based MILP and the order-exact DP serve identical request sets throughout. Operation order and purification schedule are thus substitutes, with the purification schedule the dominant factor governing feasibility under symmetric Pauli noise.