Entanglement buffering with multiple quantum memories

TL;DR

The paper analyzes entanglement buffers with one long‑lived memory and $n$ short‑lived memories (1G$n$B), deriving closed‑form expressions for availability $A$ and average consumed fidelity $\overline{F}$ under fully general purification protocols with discrete‑time dynamics. It shows that purification should be performed as frequently as possible to maximize $\overline{F}$, while often reducing $A$, and provides tight bounds and practical design guidelines for purification policies. The study reveals that simple purification strategies, such as DEJMPS, can outperform complex, fidelity‑maximizing schemes in buffering contexts, and demonstrates that policies with flags can enhance availability under certain conditions. The framework enables efficient evaluation and design of buffering policies for scalable quantum networks, with open directions on optimal ordering and policy optimization, and code available on GitHub for replication and extension.

Abstract

Entanglement buffers are systems that maintain high-quality entanglement, ensuring it is readily available for consumption when needed. In this work, we study the performance of a two-node buffer, where each node has one long-lived quantum memory for storing entanglement and multiple short-lived memories for generating fresh entanglement. Newly generated entanglement may be used to purify the stored entanglement, which degrades over time. Stored entanglement may be removed due to failed purification or consumption. We derive analytical expressions for the system performance, which is measured using the entanglement availability and the average fidelity upon consumption. Our solutions are computationally efficient to evaluate, and they provide fundamental bounds to the performance of purification-based entanglement buffers. We show that purification must be performed as frequently as possible to maximise the average fidelity of entanglement upon consumption, even if this often leads to the loss of high-quality entanglement due to purification failures. Moreover, we obtain heuristics for the design of good purification policies in practical systems. A key finding is that simple purification protocols, such as DEJMPS, often provide superior buffering performance compared to protocols that maximize output fidelity.

Figures (14)

• Figure 1: Illustration of the 1G$n$B buffering system. Entanglement generation is attempted in every bad memory (B$_1$, $\dots$, B$_n$) simultaneously in each time slot. Each memory succeeds with probability $p_\mathrm{gen}$. The good memory, G, stores entanglement, which decoheres at rate $\Gamma$. When G is full and new entanglement is generated in any of the B memories, a purification subroutine is applied with probability $q$. Entanglement is consumed from G with probability $p_\mathrm{con}$ in each time slot.
• Figure 2: Example dynamics of the 1G$n$B system. Here, the fidelity $F(t)$ of the link in the G memory is plotted against time. The vertical lines represent discretisation of time. The jumps in fidelity occur when the link is purified successfully. In between purifications, the link is subject to decoherence and the fidelity decreases. The link in the G memory is removed due to either failed purification or consumption. When there is no link in memory, $F(t) = 0$. The $j$-th consumption request arrives at time $T_{\mathrm{con}}^{(j)}$. The green tick (red crosses) represent when a consumption request is (is not) served.
• Figure 3: The upper bound on the availability is tight and it converges to the lower bound in the limit of small generation probabilities. Upper and lower bounds on the availability from (\ref{['eq.A_bounds']}), versus the effective generation probability $p_\mathrm{gen}^*=1-(1-p_\mathrm{gen})^n$. The availability can only take values within the shaded region. In this example we use $\Gamma=1$ and $p_\mathrm{con}=0.7$.
• Figure 4: The upper bound on the average consumed fidelity marks unachievable values for any purification policy. Upper and lower bounds on the average consumed fidelity $\overline F$ from (\ref{['eq.Fbounds']}), versus the effective generation probability $p_\mathrm{gen}^*=1-(1-p_\mathrm{gen})^n$. $\overline F$ can only take values within the shaded region. In this example we use $p_\mathrm{con}=0.7$.
• Figure 5: The ordering in a concatenated policy matters. Example of two different orderings when the buffered link (G) and three newly generated links (B) are used. We call ordering (a) "concatenated DEJMPS". Ordering (b) is often called "nested" Briegel1998.

Theorems & Definitions (38)

• Definition 2.1
• Definition 2.2: Availability
• Definition 2.3: Average consumed fidelity
• Theorem 1: Formula for the availability
• proof
• Theorem 2: Formula for the average consumed fidelity
• proof
• Proposition 1
• proof
• Corollary 1