Quantum entanglement is the key to quantum communications over considerable distances. The first step for entanglement distribution among quantum communication nodes is to generate link-level Einstein-Podolsky-Rosen (EPR) pairs between adjacent communication nodes. EPR pairs may be continuously generated and stored in a few quantum memories to be ready for utilization by quantum applications. A major challenge is that qubits suffer from unavoidable noise due to their interaction with the environment, which is called decoherence. This decoherence results in the known exponential decay model of the fidelity of the qubits with time, thus, limiting the lifetime of a qubit in a quantum memory and the performance of quantum applications. In this paper, we evaluate the fidelity of the stored EPR pairs under two opposite dynamical and probabilistic phenomena, first, the aforementioned decoherence and second purification, i.e. an operation to improve the fidelity of an EPR pair at the expense of sacrificing another EPR pair. Instead of applying the purification as soon as two EPR pairs are generated, we introduce a Purification scheme Beyond the Generation time (PBG) of two EPR pairs. We analytically show the probability distribution of the fidelity of stored link-level EPR pairs in a system with two quantum memories at each node allowing a maximum of two stored EPR pairs. In addition, we apply a PBG scheme that purifies the two stored EPR pairs upon the generation of an additional one. We finally provide numerical evaluations of the analytical approach and show the fidelity-rate trade-off of the considered purification scheme.
Quantum entanglement is the key to quantum communications over considerable distances. The first step for entanglement distribution among quantum communication nodes is to generate link-level Einstein-Podolsky-Rosen (EPR) pairs between adjacent communication nodes. EPR pairs may be continuously generated and stored in a few quantum memories to be ready for utilization by quantum applications. A major challenge is that qubits suffer from unavoidable noise due to their interaction with the environment, which is called decoherence. This decoherence results in the known exponential decay model of the fidelity of the qubits with time, thus, limiting the lifetime of a qubit in a quantum memory and the performance of quantum applications. In this paper, we evaluate the fidelity of the stored EPR pairs under two opposite dynamical and probabilistic phenomena, first, the aforementioned decoherence and second purification, i.e. an operation to improve the fidelity of an EPR pair at the expense of sacrificing another EPR pair. Instead of applying the purification as soon as two EPR pairs are generated, we introduce a Purification scheme Beyond the Generation time (PBG) of two EPR pairs. We analytically show the probability distribution of the fidelity of stored link-level EPR pairs in a system with two quantum memories at each node allowing a maximum of two stored EPR pairs. In addition, we apply a PBG scheme that purifies the two stored EPR pairs upon the generation of an additional one. We finally provide numerical evaluations of the analytical approach and show the fidelity-rate trade-off of the considered purification scheme.
The first step for entanglement distribution among quantum communication nodes is to generate link-level Ein-stein-Podolsky-Rosen (EPR) pairs between adjacent communication nodes. EPR pairs may be continuously generated and stored in a few quantum memories to be ready for utilization by quantum applications. A major challenge is that qubits suffer from unavoidable noise due to their interaction with the environment, which is called decoherence. This decoherence results in the known exponential decay model of the fidelity of the qubits with time, thus, limiting the lifetime of a qubit in a quantum memory and the performance of quantum applications. In this paper, we evaluate the fidelity of the stored EPR pairs under two opposite dynamical and probabilistic phenomena, first, the aforementioned decoherence and second purification, i.e. an operation to improve the fidelity of an EPR pair at the expense of sacrificing another EPR pair. Instead of applying the purification as soon as two EPR pairs are generated, we introduce a Purification scheme Beyond the Generation time (PBG) of two EPR pairs. We use discrete time Markov chain (DTMC) approach to analytically show the probability distribution of the fidelity of stored link-level EPR pairs in a system with two quantum memories at each node allowing a maximum of two stored EPR pairs. In addition, we apply a PBG scheme that purifies the two stored EPR pairs upon the generation of an additional one. We finally provide numerical evaluations of the analytical approach and show the fidelity-rate trade-off of the considered purification scheme.
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.
Entanglement generation over large distances is a challenging task due to photon loss, which grows exponentially with link length (e.g., optical fiber). Moreover, EPR pair generation over noisy channels results in imperfect states. Thus, a link is associated with a success probability and an initial fidelity for successfully-generated entanglement. Over time, fidelity de-creases due to environmental noise. Entanglement purification is a way of probabilistically increasing state fidelity. Traditionally, purification protocols perform the following steps: generate two or more EPR pairs between two nodes, execute a series of quantum gates on both sides, and exchange results via classical messages. In this work, we propose a twist on the original entanglement pumping scheme, wherein a fixed number of purification steps are performed successively, before the classical information exchange. This modification introduces optimism to the overall procedure, such that classical communication is performed only at the end, to check the measurement results. The protocol is also optimistic about entanglement generation and does not wait for heralding signals before attempting purification. We study the effect of being optimistic on fidelity and the waiting time to generate an entangled pair as a function of the distance between network nodes. We observe an improvement in both fidelity and expected waiting time. We also study the effect of the number of purification steps on fidelity and latency and observe that typically no more than two or three purification steps are needed when limited by only two memories.
Noise and photon loss encountered on quantum channels pose a major challenge for reliable entanglement generation in quantum networks. In near-term networks, heralding is required to inform endpoints of successfully generated entanglement. If after heralding, entanglement fidelity is too low, entanglement purification may be utilized to probabilistically increase fidelity. Traditionally, purification protocols proceed as follows: generate heralded EPR pairs, execute a series of quantum operations on two or more pairs between two nodes, and classically communicate results to check for success. Purification may require several rounds while qubits are stored in memories, vulnerable to decoherence. In this work, we explore notions of optimistic purification, wherein classical communication required for heralding and purification is delayed, possibly to the end of the process. Optimism reduces the overall time EPR pairs are stored in memory, increasing fidelity while possibly decreasing EPR pair rate due to decreased heralding and purification failure. We apply optimism to the entanglement pumping scheme, ground- and satellite-based EPR generation sources, and current state-of-the-art purification circuits that include several measurement and purification checkpoints. We evaluate performance in view of a number of parameters, including link length, EPR source rate and fidelity; and memory coherence time. We show that while our optimistic protocol increases fidelity, the traditional approach may even decrease fidelity for longer distances. We study the trade-off between rate and fidelity under entanglement-based QKD, and find that optimistic schemes can yield higher rates compared to non-optimistic counterparts, with most advantages seen in scenarios with low initial fidelity and short coherence times.
The quantum Internet envisions a network where information is transmitted through entanglement, with Einstein-Podolsky-Rosen (EPR) pairs serving as one of the fundamental carriers. In this work, we propose a framework for dimensioning quantum memories capable of storing distilled EPR pairs useful to transmitting and manage quantum error correcting codes. Using a Markov chain model, we capture the stochastic evolution of stored entangled states in quantum memories, linking memory performance to system parameters such as technology characteristics and initial entanglement fidelity. Building on this framework, we provide analytical tools and design principles for optimizing memory architectures that preserve high-fidelity entanglement over time, ensuring the availability of encoded quantum resources necessary for several operations in future quantum Internet infrastructures transmitting EPR packets.
Quantum networks crucially rely on the availability of high-quality entangled pairs of qubits, known as entangled links, distributed across distant nodes. Maintaining the quality of these links is a challenging task due to the presence of time-dependent noise, also known as decoherence. Entanglement purification protocols offer a solution by converting multiple low-quality entangled states into a smaller number of higher-quality ones. In this work, we introduce a framework to analyse the performance of entanglement buffering setups that combine entanglement consumption, decoherence, and entanglement purification. We propose two key metrics: the availability, which is the steady-state probability that an entangled link is present, and the average consumed fidelity, which quantifies the steady-state quality of consumed links. We then investigate a two-node system, where each node possesses two quantum memories: one for long-term entanglement storage, and another for entanglement generation. We model this setup as a continuous-time stochastic process and derive analytical expressions for the performance metrics. Our findings unveil a trade-off between the availability and the average consumed fidelity. We also bound these performance metrics for a buffering system that employs the well-known bilocal Clifford purification protocols. Importantly, our analysis demonstrates that, in the presence of noise, consistently purifying the buffered entanglement increases the average consumed fidelity, even when some buffered entanglement is discarded due to purification failures.