Carrier-Assisted Entanglement Purification

TL;DR

This work introduces the Carrier-Assisted Entanglement Purification Protocol (CAEPP), a practical entanglement distillation method that requires only two quantum memories for a single shared pair and a single traveling qubit carrier, reducing memory and coherent-operation overhead. The authors show that CAEPP can purify noisier entanglement when the carrier channel is ideal, and that performance degrades gracefully under noisy carriers; crucially, employing multiple carriers with stabilizer codes (mCAEPP) can push the convergent fidelity toward 1, enabling reliable ebits even through noisy channels. They establish a formal update rule linking Bell-diagonal coefficients before and after purification, derive fidelity gain conditions, and compare CAEPP with two-way purification, highlighting practical advantages such as reduced memory demands and fewer measurements. The framework is further extended to multipartite entanglement purification (e.g., GHZ states), suggesting CAEPP as a scalable, hardware-friendly alternative for near-term quantum networks and repeaters. Overall, the work advances entanglement distillation by trading off quantum memory and measurement hardware for controlled carrier transmission, bringing robust long-distance entanglement closer to practical realization.

Abstract

Entanglement distillation, a fundamental building block of quantum networks, enables the purification of noisy entangled states shared among distant nodes by local operations and classical communication. Its practical realization presents several technical challenges, including the storage of quantum states in quantum memory and the execution of coherent quantum operations on multiple copies of states within the quantum memory. In this work, we present an entanglement purification protocol via quantum communication, namely a carrier-assisted entanglement purification protocol, which utilizes two elements only: i) quantum memory for a single-copy entangled state shared by parties and ii) single qubits travelling between parties. We show that the protocol, when single-qubit transmission is noiseless, can purify a noisy entangled state shared by parties. When single-qubit transmission is noisy, the purification relies on types of noisy qubit channels; we characterize Pauli channels such that the protocol works for the purification. We address this limitation by using multiple carrier qubits, and show that for any depolarizing channel with channel fidelity greater than 1/2, the protocol's fixed-point fidelity approaches unity as the number of carrier increases. Our results significantly reduce the experimental overhead needed for distilling entanglement, such as quantum memory and coherent operations, making long-distance pure entanglement closer to a practical realization.

Figures (13)

• Figure 1: The CAEPP with a single-qubit carrier is shown. When two parties share a state $\rho$, Alice prepares an ancilla qubit in a state $|0\rangle$, applies a CNOT gate as well as a local unitary $V_A$ as an encoding, and sends a carrier qubit to Bob, who applies a decoding $V_B$ and a CNOT gate. Once a measurement outcome on a carrier qubit is $0$, two parties accept a resulting state, denoted by $\rho_{\mathrm{out}}$.
• Figure 2: The CAEPP has two channels, one for transmitting a carrier against a noisy channel, and the other for sharing an entangled pair. For fair comparisons with TWEPPs, let us assume that the two channels are identical and that both are depolarizing channels. (a) The fidelity of a shared entangled state increases by a single-qubit carrier. For instance, a pair with $F=p_{00}=0.75$ (black dot), a single round of the CAEPP increases it to $0.788$ (red dot), and then the next one to $0.841$ (green dot). The fidelity converges to $F_{\star}\approx 0.863$. (b) The entanglement fidelity (solid line) increases quickly so that it is sufficiently close to the maximal convergent fidelity after four rounds. The first two rounds are more efficient than the next two rounds. The total success probability (dotted line) of accepting an entangled pair decreases. For instance, when an initial fidelity is $F=0.75$, the total success probability after four rounds is about $0.3$ (orange line).
• Figure 3: The CAEPP exploits a noisy channel, a general Pauli channel in \ref{['new_biased_chan']}, to share an entangled pair and transmit a single-qubit carrier. Compared to the case of depolarizing channels in Fig. \ref{['fig:depol']}, one can find that the maximum convergent fidelity is higher as the $Z$-error rate is lower. (Left) The entanglement fidelity increases by exploiting single-qubit carriers. (Right) Four rounds of the CAEPP reach an entanglement fidelity (solid line), sufficiently close to the maximal convergent fidelity $F_{\star}$. The total success probability decreases as the CAEPP applies more single-qubit carriers. For instance, for an initial fidelity $F=0.85$, the CAEPP increases it up to $F=0.95$ after four rounds. The total success probability is about $0.5$ (blue line).
• Figure 4: The CAEPP with noisy transmission of a carrier against a flip channel is shown. In this case, where the $Z$-error rate does not occur in a channel, repeating rounds of the CAEPP achieves the purification of an ebit $F_\star=1$.
• Figure 5: A successful round of the CAEPP with two carriers, using the check operators $\{X_1 X_2,\, Z_0 Z_1 Z_2\}$, is shown. Alice and Bob start from an input state $\rho$. After Pre-processing on a shared pair, Alice performs Encoding and sends the two carriers through the same noisy channel $\mathcal{N}$. Bob performs Decoding and measures two carriers; the shared state is kept only if the measurement outcome is $00$.