Robust Quantum Teleportation Against Noise Using Weak Measurement and Flip Operations

TL;DR

This work addresses the challenge of maintaining high teleportation fidelity in noisy quantum channels. It proposes a four-qubit entangled-state teleportation protocol that interleaves weak measurements with flip operations before transmission and reversal operations after transmission, comparing two WM-WMR schemes across amplitude-damping, bit-flip, and phase-flip noise. The authors derive explicit final states and fidelities for both WM protocols, demonstrating substantial fidelity gains—most notably under amplitude damping where $F_{max}$ approaches unity for certain parameter choices, and meaningful improvements under BFC and PFC as well. The results suggest that optimized WM strategies can significantly enhance noise resilience in quantum communication and motivate extensions to higher-dimensional systems and larger networks.

Abstract

This study presents an improved quantum teleportation protocol designed to enhance fidelity in noisy environments by combining weak measurements (WMs) with flip and reversal operations. In our scheme, Alice prepares a four-qubit entangled state and shares one of the entangled qubits with Bob, which serves as the quantum channel for teleporting an arbitrary single-qubit state. Since the communication channel is subject to noise, Alice performs a weak measurement on the shared qubit before transmission to reduce the impact of decoherence. Building upon existing WM-flip-reversal frameworks, we propose a modified weak measurement and reversal (WMR) protocol tailored for different noises in a four-qubit entangled system. The approach applies WM and flip operations prior to transmission to enhance resilience against noise, followed by corresponding reversal operations after transmission to recover the original quantum state. We systematically compare the performance of our proposed WMR protocol with the previously proposed WM-flip-reversal method under three common noise models: amplitude damping channel (ADC), phase flip channel (PFC), and bit flip channel (BFC). Our analysis reveals that the modified WMR scheme achieves significantly higher teleportation fidelity and improved robustness, particularly in bit flip noise environments. These findings highlight the potential of optimized weak measurement strategies for developing more reliable and noise-tolerant quantum communication protocols.

Figures (7)

• Figure 1: Teleportation fidelity for ADC with weak measurement protocol-I in Eq. (\ref{['psi_final_adcI']}).We compare ADC for $r=0.5$ and $r=0.9$ and observe that the protocol provides a higher fidelity than the unprotected teleportation protocol (shown by the gray region) for a range of parameter values.
• Figure 2: Teleportation fidelity for BFC with weak measurement protocol-I in Eq. (\ref{['psi_final_adcI']}).We compare BFC for $r=0.5$ and $r=0.9$ and observe that the protocol provides a higher fidelity than the unprotected teleportation protocol (shown by the gray region) for a range of parameter values.
• Figure 3: Teleportation fidelity for PFC with weak measurement protocol-I in Eq. (\ref{['psi_final_adcI']}).We compare PFC for $r=0.5$ and $r=0.9$ and observe that for $r=0.5$ the fidelity is same as the unprotected teleportation protocol (shown by the gray region) but for $r=0.9$ the fidelity is higher for a range of parameter values.
• Figure 4: Teleportation fidelity for ADC with weak measurement protocol-II in Eq. (\ref{['new_WM_POVM']}).We compare ADC for $r=0.5$ and $r=0.9$ and observe that the protocol provides a higher fidelity than the unprotected teleportation protocol (shown by the gray region) for a range of parameter values.
• Figure 5: Teleportation fidelity for BFC with weak measurement protocol-II in Eq. (\ref{['new_WM_POVM']}). We compare BFC for $r=0.5$ and $r=0.9$ and observe that for $r=0.5$ the protocol provides a similiar fidelity as for the unprotected teleportation protocol(shown by the gray region) but for $r=0.9$ it provides higher fidelity than the unprotected protocol for a range of parameter values.