Entanglement distillation based on Hamiltonian dynamics

TL;DR

This work introduces the Hamiltonian entanglement distillation protocol, which exploits the intrinsic information scrambling generated by random time evolution under native Hamiltonians, and establishes a quantitative connection between output fidelity and Out-of-Time-Order Correlators, showing that efficient scrambling directly implies good distillation performance.

Abstract

Efficient entanglement distillation is a central task in quantum information science and future quantum networks. At the core of distillation protocols are the quantum error correction and detection schemes which enhance the fidelity of entangled pairs. Conventional protocols focus on digital systems, which typically require complicated compiled circuits, high-fidelity multi-qubit operations and delicate pulse-level control that impose high demands on near-term hardware. Crucially, the leading physical platforms for quantum networks, trapped ions and neutral atoms, are governed by native many-body Hamiltonians inherently suited for analog, continuous-time evolution. Adopting these natural dynamics is simpler than engineering digital logic via delicate pulse-level control. Motivated by this experimental reality, we seek to leverage the intrinsic analog capabilities for efficient entanglement distillation. In this work, we introduce the Hamiltonian entanglement distillation protocol, which exploits the intrinsic information scrambling generated by random time evolution under native Hamiltonians. We establish a quantitative connection between output fidelity and Out-of-Time-Order Correlators, showing that efficient scrambling directly implies good distillation performance. Since generic Hamiltonians are naturally efficient scramblers, the capability for distillation is ubiquitous: almost all Hamiltonians in the Hilbert space suffice for high-fidelity distillation. Numerical simulations of representative Rydberg-atom and trapped-ion systems further confirm that robust performance could be achieved using only short-range interactions and evolution times feasible in current experiments. By avoiding the complexity of digital circuit control, our approach substantially relaxes experimental requirements, providing a scalable route to entanglement engineering on current analog quantum platforms.

Figures (7)

• Figure 1: Distillation performance as a function of the number of measurement qubits. The solid line with circle markers denotes the output fidelity, while the dashed line with cross markers denotes the yield. We consider a ten-qubit Hamiltonian with local depolarizing noise of strength $p=0.2$.
• Figure 2: Distillation performance as a function of the depolarizing noise strength. The solid line with circle markers denotes the output fidelity, while the dashed line with cross markers denotes the yield. We consider a six-qubit Hamiltonian with three measurement qubits.
• Figure 3: Finite-time distillation performance for trapped-ion and Rydberg Hamiltonians. The characteristic evolution times are at the microsecond ($\mu$s) scale for the Rydberg Hamiltonian and at the millisecond (ms) scale for the trapped-ion Hamiltonian. The solid line with circle markers denotes the output fidelity, while the dashed line with cross markers denotes the yield.
• Figure 4: Distillation performance with and without Pauli twirling. The solid line with circle markers corresponds to the case with Pauli twirling, while the dashed line with triangle markers corresponds to the case without twirling.
• Figure 5: Tolerable error rates under varying conditions: (a) asymptotic behavior as a function of the measurement qubit ratio $m/n$; (b) performance for finite system sizes where $n, m \leq 100$.

Theorems & Definitions (19)

• Definition 1
• Theorem 1
• Lemma 1
• Theorem 2
• Theorem 3
• Theorem 4
• Corollary 1
• Definition 2: Mutually unbiased bases
• Definition 3
• Theorem : Theorem \ref{['thm:diagonal_twirling']}