bibkey: inestaetal2026entanglementbuffering
authors: Álvaro G. Iñesta; Bethany Davies; Sounak Kar; Stephanie Wehner
year: 2026
title: "Entanglement buffering with multiple quantum memories"
doi: 10.1038/s41534-025-01161-3
url: https://arxiv.org/abs/2502.20240v1
claim: "The paper models an entanglement buffer with one long-lived memory and n short-lived generation memories, with probabilistic generation, consumption, depolarising decay and probabilistic purification governed by coefficients a_k, b_k, c_k, d_k; it derives closed-form formulas for the availability and the average consumed fidelity, proves that the availability is non-increasing in the purification probability q, gives policy-independent bounds, and conjectures that the availability at q = 1 of the always-failing policy (c_k = d_k = 0) is a tight lower bound for every purification policy."
strata_touched:
  - D5/S3/Quantum/Decoherence/EntanglementBufferAvailabilityLowerBound
license: citation-only
triage: anchor

Entanglement buffering with multiple quantum memories

Á. G. Iñesta, B. Davies, S. Kar and S. Wehner, arXiv:2502.20240v1 (only version); npj Quantum Information 12 (2026), 64. Quotations are from the v1 TeX source; displayed macros are expanded without changing the wording.

The decay of the buffered link:

The entangled link stored in G is subject to depolarising noise with memory lifetime $1/\Gamma$, which causes an exponential decay in fidelity with rate $\Gamma$. That is, if the link in memory has an initial fidelity $F$, after time $t$ this reduces to $F\mapsto \left(F-\frac{1}{4}\right)e^{-\Gamma t}+\frac{1}{4}.$

Purification policies:

The purification policy $\pi$ is a function that indicates the purification protocol that must be used when $k$ links are generated in the B memories, $\pi :k\in \{1,\dots ,n\}\mapsto \pi (k)\in {\mathcal{P}}_{k+1}$, where ${\mathcal{P}}_m$ is the set of all $m$-to-1 purification protocols.

The purification protocol updates the fidelity of the buffered link from $F$ to $J_k(F)$, where $J_k(F)=\frac{1}{4}+\frac{a_k({\rho }_{\mathrm{new}})\left(F-\frac{1}{4}\right)+b_k({\rho }_{\mathrm{new}})}{c_k({\rho }_{\mathrm{new}})\left(F-\frac{1}{4}\right)+d_k({\rho }_{\mathrm{new}})}.$

The protocol succeeds with probability $p_k(F)=c_k({\rho }_{\mathrm{new}})\left(F-\frac{1}{4}\right)+d_k({\rho }_{\mathrm{new}})$, otherwise all of the links (including the buffered one) are discarded and the G memory becomes empty.

Availability (Definition def.A):

The availability $A$ is the probability that there is an entangled link present in memory G when a consumption request arrives.

Theorem 1 (theorem.A) states $A=\mathbb{E}[T_{\mathrm{occ}}]/(\mathbb{E}[T_{\mathrm{gen}}]+\mathbb{E}[T_{\mathrm{occ}}])$ a.s., with $\mathbb{E}[T_{\mathrm{gen}}]=1/(1-(1-p_{\mathrm{gen}}{)}^n)$ and $$\mathbb{E}[T_{\mathrm{occ}}]=[(1-\stackrel{)(1-D}{A})-\stackrel{C}{B}]\stackrel{1-A}{P}+\stackrel{(Fnew-41),\; where\; P}{C}=p_{\mathrm{con}}+q(1-(1-p_{\mathrm{gen}}{)}^n)(1-p_{\mathrm{con}})$$

Appendix C, on the admissible coefficients:

Since $p_k$ is a probability, we must enforce $0\le p_k\le 1$.

This output fidelity must also be between $1/4$ (fully depolarized state) and $1$ (perfect Bell pair).

The conjecture (after Corollary 1):

Unlike the upper bound, we note that the lower bound from (\ref{eq.A_bounds}) has not yet shown to be tight. We believe that the availability at $q=1$ of a policy that always fails purification ($c_k=d_k=0$, $\forall k$) constitutes a tight lower bound for any other purification policy. We leave this proof as future work.

Verified locator

Source: https://arxiv.org/abs/2502.20240v1

• URL: https://arxiv.org/abs/2502.20240v1 (the e-print is a tar archive; member main.tex, md5 c1b5c2a56b45349a94ac22e6fde7bd87, 2402 lines):
  • the depolarising decay, l. 223–228;
  • the purification policy, the jump function and the success probability, l. 247–265;
  • availability, l. 344–354;
  • Theorem 1, l. 378–415;
  • Corollary 1 and the conjecture, l. 479–502;
  • the admissible coefficients, Appendix C, l. 1734–1767.
• DOI: 10.1038/s41534-025-01161-3 (https://doi.org/10.1038/s41534-025-01161-3; Crossref lists npj Quantum Information, volume 12, issue 1, article 64, published 20 February 2026). The journal text keeps the conjecture and its “future work” sentence verbatim.