Experimental Quantum Channel Purification

Abstract

Quantum networks, which integrate multiple quantum computers and the channels connecting them, are crucial for distributed quantum information processing but remain inherently susceptible to channel noise. Channel purification emerges as a promising technique for suppressing noise in quantum channels without complex encoding and decoding operations, making it particularly suitable for remote quantum information transmission in optical systems. In this work, we introduce an experimental setup for efficient channel purification, harnessing the spatial and polarization properties of photons. Our design employs two Fredkin gates to enable coherent interference between independent noise channels, achieving effective noise suppression across a wide range of noise levels and types. Through application to entanglement distribution, our protocol demonstrates a superior capability to preserve entanglement against channel noise compared to conventional entanglement purification methods.

Figures (4)

• Figure 1: Difference between entanglement purification and channel purification. (a) In a state distribution task, as demonstrated with a bipartite one, even if the noise is primarily introduced by a single channel (from the Sender to Bob), entanglement purification requires operations over all parties, leading to high resource consumption. (b) A channel purification protocol specifically targets the noise channel and suppresses noise with only local operations. The protocol does not require operations on the other channels from the sender to A$_1$, A$_2$, or A$_3$. Furthermore, channel purification can operate on a single copy of the distributed state, and has no requirement for quantum memory to store multiple noisy states.
• Figure 2: Channel purification protocol and experimental setup. (a) Quantum circuit of our channel purification protocol, where $H$ represents the Hadamard gate and $\rho_{\mathrm{m}}$ represents the maximally mixed state. Two noise channels, $\mathcal{C}_1$ and $\mathcal{C}_2$, are sandwiched by two Fredkin gates. (b) The circuit implemented in the linear optical system. A Fredkin-like gate is realized by the spatial beam splitter (SBS). Control register encoded in spatial DoF directs the photon to different paths. Qubits in different DoF from the same photon are marked as the same color. (c) Detailed experiment setup. In order to distinguish two photons, we mark photons of the main and ancillary registers with red and orange colors, respectively. The separation between these two light paths is 3 $\mathrm{mm}$. QWP-HWP-QWP combinations are employed to compensate for phase shifts introduced by BS. A total of 8 superconducting nanowire single-photon detectors are used for detection. BD: beam displacer; BS: beam splitter; HWP: half wave plate; QWP: quarter wave plate; TC quartz: quartz for time compensation; PBS: polarizing beam splitter.
• Figure 3: Experimental results for channel purification. (a) Pauli transfer matrices (magnitude) of the initial channels and the purified channels. (b) Average state fidelities between initial and purified channels with the ideal noiseless channel. Error bar here is about $10^{-4}$.
• Figure 4: Experimental results for entanglement distribution. Fidelity is quantified as the overlap between the distributed state and the Bell state $\ket{\Phi^+}$. The simulated lines are based on the initial state tomographic data without introducing noise. The fidelity larger than $0.5$ indicates the existence of entanglement. In the range of $p$ labeled by the red rectangle, the entanglement shared by two parties is destroyed by the noise channel, while it can be preserved by channel purification.