Nonlocality distillation can outperform entanglement distillation

Abstract

Given the goal of maximizing CHSH violation, we compare the optimal strategies of entanglement and nonlocality distillation. In the limit of the number of copies of the shared state, entanglement distillation is guaranteed to work by generating a Bell state. For a small number of copies of the state, we show that nonlocality distillation can achieve a higher CHSH value, even though optimal entanglement distillation requires communication. Nonlocality distillation not only outperforms entanglement distillation but also demonstrates superior resource efficiency across multiple metrics for quantum resource estimation.

Figures (6)

• Figure 1: Comparison between entanglement distillation and nonlocality distillation for $n=2, 3$ and $4$ for pure states. The results indicate that nonlocality distillation outperforms entanglement distillation for a specific range of $p$, but this advantage vanishes beyond three copies.
• Figure 2: Nonlocality distillation bounds for one, two and three copies of the mixed state $\rho$.
• Figure 3: Circuit for preparing two copies of the initial quantum state $\ket{\Psi}$. The fifth qubit is n ancilla for the entanglement distillation process.
• Figure 4: The optimal measurement circuit for entanglement distillation. The optimal CHSH measurements are performed on the first qubit of each party (qubits $0$ and $3$ in Figure \ref{['ed:circ']}), since the Bell pair is generated between these qubits.
• Figure 5: The circuit for optimal nonlocality distillation measurements given by Equation \ref{['eq:meas']}.

Theorems & Definitions (2)

• Theorem 1
• Theorem 2