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arXiv:2606.14908 · Quantum Science and Technology

Optimising Entanglement Distillation Policies

Jigyen Bhavsar, Rajni Bala, Siddhartha Santra

quant-phSubmitted Jun 12, 2026• Announced Jun 16, 2026• 0 citations
v1 · Jun 12, 2026v2 · Jul 3, 2026
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Abstract

Entanglement distillation is a fundamental operation in quantum information processing used to obtain higher-fidelity entangled pairs from a supply of less entangled quantum states using local operations aided by classical communication (LOCC). In a physically relevant setting, where states with an initial fidelity of $f_0$, probabilistically generated over multiple, $m$, memory pairs distributed between two parties, Alice and Bob, are pairwise distilled, the optimal policy identifies the system-configuration dependent sequence of entanglement generation and distillation operations that need to be performed in order to minimize the expected time to reach some target fidelity $f_T>f_0$. Here, we formulate and systematically analyze this task as a Markov decision problem and using a value iteration algorithm, obtain optimal deterministic policies that minimize the expected waiting time required to reach a target fidelity. Our results show that the expected waiting time under the optimal policy decreases with increasing generation probability $p$ and number of quantum memories $m$ - as expected. In contrast, it exhibits non-monotonic behavior with respect to $f_0$ for a fixed fidelity gap, $(Δf = f_T-f_0)$. While the optimal policy consistently outperforms baseline policies such as the greedy, nested and entanglement pumping policies, its relative advantage is regime-dependent, being determined by the system parameters ($p,f_0,f_T,m$), and exhibits a nontrivial dependence on the fidelity gap $Δf$. Our results highlight the value of formulating entanglement distillation as a Markov decision problem, enabling the systematic design of policies that achieve target fidelity thresholds for quantum information tasks in realistic resource-constrained settings.

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Entanglement distillation is a fundamental operation in quantum information processing used to obtain higher-fidelity entangled pairs from a supply of less entangled quantum states using local operations aided by classical communication (LOCC). In a physically relevant setting, where states with an initial fidelity of f0f_0f0​, probabilistically generated over multiple, mmm, memory pairs distributed between two parties, Alice and Bob, are pairwise distilled, the optimal policy identifies the system-configuration dependent sequence of entanglement generation and distillation operations that need to be performed in order to minimize the expected time to reach some target fidelity fT>f0f_T>f_0fT​>f0​. Here, we formulate and systematically analyze this task as a Markov decision problem and using a value iteration algorithm, obtain optimal deterministic policies that minimize the expected waiting time required to reach a target fidelity. Our results show that the expected waiting time under the optimal policy decreases with increasing generation probability ppp and number of quantum memories mmm - as expected. In contrast, it exhibits non-monotonic behavior with respect to f0f_0f0​ for a fixed fidelity gap, (Δf=fT−f0)(Δf = f_T-f_0)(Δf=fT​−f0​). While the optimal policy consistently outperforms baseline policies such as the greedy, nested and entanglement pumping policies, its relative advantage is regime-dependent, being determined by the system parameters (p,f0,fT,mp,f_0,f_T,mp,f0​,fT​,m), and exhibits a nontrivial dependence on the fidelity gap ΔfΔfΔf. Our results highlight the value of formulating entanglement distillation as a Markov decision problem, enabling the systematic design of policies that achieve target fidelity thresholds for quantum information tasks in realistic resource-constrained settings.
The quantum switch is a vital component for the development of the quantum internet. In an entanglement distribution network, the function of a quantum switch is to generate elementary entanglement with its clients followed by entanglement swapping to distribute end-to-end entanglement of sufficiently high fidelity between clients. The threshold on entanglement fidelity is any quality of service requirement specified by the clients as dictated by the application they run on the network. We consider a discrete time model for a quantum switch that attempts generation of fresh elementary entanglement with clients in each time step in the form of maximally entangled qubit pairs, or Bell pairs, which succeed probabilistically; the successfully generated Bell pairs are stored in noisy quantum memories until they can be swapped. We focus on establishing the value of entanglement distillation of the stored Bell pairs prior to entanglement swapping in presence of their inevitable aging, i.e., decoherence: For a simple instance of a switch with two clients, an exponential decay of entanglement fidelity, and a wellknown probabilistic but heralded two-to-one distillation protocol, given a threshold end-to-end entanglement fidelity, we use the Markov Decision Processes framework to identify the optimal action policy - to wait, to distill, or to swap that maximizes throughput. We compare the switch's performance under the optimal distillation-enabled policy with that excluding distillation. Simulations of the two policies demonstrate the improvements that are possible in principle via optimal use of distillation with respect to average throughput, average fidelity and jitter of end-to-end entanglement, as functions of fidelity threshold. Our model thus helps capture the role of entanglement distillation in mitigating the effects of decoherence in a quantum switch in an entanglement distribution network, adding to the growing literature on quantum switches.
Protocols for distributed quantum systems commonly require the simultaneous availability of nnn entangled states, each with a fidelity above some fixed minimum FappF_{\mathrm{app}}Fapp​ relative to the target maximally-entangled state. However, the fidelity of entangled states degrades over time while in memory. Entangled states are therefore rendered useless when their fidelity falls below FappF_{\mathrm{app}}Fapp​. This is problematic when entanglement generation is probabilistic and attempted in a sequential manner, because the expected completion time until nnn entangled states are available can be large. Motivated by existing entanglement generation schemes, we consider a system where the entanglement generation parameters (the success probability ppp and fidelity FFF of the generated entangled state) may be adjusted at each time step. We model the system as a Markov decision process, where the policy dictates which generation parameters (p,F)(p,F)(p,F) to use for each attempt. We use dynamic programming to derive optimal policies that minimise the expected time until nnn entangled states are available with fidelity greater than FappF_{\mathrm{app}}Fapp​. We observe that the advantage of our optimal policies over the selected baselines increases significantly with nnn. In the parameter regimes explored, which are based closely on current experiments, we find that the optimal policy can provide a speed-up of as much as a factor of twenty over a constant-action policy. In addition, we propose a computationally inexpensive heuristic method to compute policies that perform either optimally or near-optimally in the parameter regimes explored. Our heuristic method can be used to find high-performing policies in parameter regimes where finding an optimal policy is intractable.
Entanglement distillation and entanglement swapping have been extensively studied assuming perfect quantum memories. However, near-term quantum networks will be fundamentally limited by quantum memories with a finite coherence time, resulting in complex choices for the timing and ordering of these operations. In this work, we study entanglement distillation and entanglement swapping at the level of the elementary building blocks of noisy quantum repeater networks, with the goal of elucidating the fundamental tradeoffs induced by memory decoherence. First, we focus on a minimal one-hop setting, where we analytically compare ``distill-as-soon-as-possible'' and ``distill-as-late-as-possible'' strategies against a baseline strategy that simply discards the older entangled state. We find that in the low memory coherence time regime, discarding the older entangled state achieves higher expected output fidelity, while in the high coherence time regime, delaying distillation until the end achieves the highest expected output fidelity and, over most of the deadline range, the highest weighted coherent information, at the expense of a lower success probability. We then extend our analysis to two-hop repeater chains using Monte Carlo simulation. In this setting, we find that the highest weighted coherent information is achieved by strategies that defer distillation to the end of the time window, with \textsf{Distill-ALAP-then-Swap-ALAP} and \textsf{Swap-ASAP-then-Distill-ALAP} leading at different operating points, while \textsf{Discard-Oldest-then-Swap} never reaches positive weighted coherent information in any regime tested. Together, these results clarify how decoherence reshapes the optimal operation timing in quantum networks and provide instructive insights into the link-level principles that govern larger-scale architectures.
Quantum repeaters are essential for achieving long-distance quantum communication due to photon loss, which grows exponentially with the channel distance. Current quantum repeater generations use entanglement distillation protocols, where the decision of when to perform distillation depends on either local or global knowledge. Recent approaches for quantum repeaters, such as Mantri et al. (arXiv:2409.06152), consider using deterministic local decision policies for entanglement distillation. We ask whether global deterministic policies outperform local ones in terms of communication rate. We simulate equidistant repeater chains, assisted by two-way classical communication, and compare local and global policies for distillation decisions, spanning large distances and varying network and hardware parameters. Our findings show that global deterministic policies consistently outperform these local ones, and in some cases, determine whether secret communication is possible. For large repeater chains (N>512N>512N>512), global policies improve SKR by two orders of magnitude. These results suggest that local distillation decisions in quantum repeater chains may not be optimal, and may inform future protocol design.
We recently proposed an entanglement distillation protocol based on local operations and classical communication that probabilistically and universally distills a maximally entangled Bell pair from multiple copies of an unknown two-qubit state [Phys. Rev. Lett. 135, 260202 (2025)]. Here, we investigate the robustness of this protocol against imperfections in its implementation. We consider several incoherent and coherent gate-error models, as well as measurement readout errors, and determine the regimes in which distillation enhances the fidelity with the target Bell state. We find that the protocol remains effective over substantial error ranges, although its robustness depends strongly on the type of error. We further analyze asymmetric errors between the two parties and identify conditions under which complementary postselection outcomes yield identical distillation dynamics, allowing the success probability to be enhanced.
Near-term and early fault-tolerant quantum computing architectures are expected to exhibit highly non-uniform error rates. In particular, local operations within a chip can be substantially more reliable than operations connecting different chips or dilution refrigerators. Such inter-module operations can therefore become a dominant bottleneck, even when quantum error correction is applied. Entanglement distillation provides a natural way to trade additional operations and qubits for higher-fidelity entanglement. Standard distillation protocols, however, are usually formulated in an LOCC resource model, in which several noisy Bell pairs are generated initially and all subsequent processing consists only of local operations and classical communication. Here, we consider a generalized model tailored to modular quantum computing hardware, in which the two modules have access to high-fidelity local operations and to repeated uses of the same noisy inter-module entangling operation during the protocol. We develop practical small-scale entanglement distillation protocols designed to minimize both space and time overhead. Remarkably, our main protocol requires only two qubits per module, yet achieves quadratic error suppression of inter-module errors, assuming local operations are much cleaner. Compared with existing small-scale protocols, our space-optimal protocol provides more space- and time-efficient quadratic error suppression and achieves the best performance in our simulations and experiments on noisy links of current superconducting quantum processors. These results suggest that inter-module-gate-assisted entanglement distillation can be a practical primitive for overcoming noisy links in modular quantum computing architectures.