量子纠缠的极强不可逆性

中文摘要 AI 辅助

量子纠缠的操控本质上是不可逆的：一些混合纠缠态需要纯纠缠才能制备，尽管通过局域操作和经典通信（LOCC）无法从它们中恢复出任何纯纠缠。已知这种不可逆性即使在不产生纠缠的最大操作类别下依然存在，揭示了纠缠理论与热力学之间的根本区别。我们构造了这样的情况：任何恢复可逆性的尝试必然会产生随副本数量指数增长的误差。从技术上讲，我们证明了指数强逆蒸馏纠缠与指数强逆纠缠成本之间存在严格分离。我们的结果解决了Lami和Regula（《自然·物理》19, 184-189 (2023)）提出的猜想，并通过证明纠缠的不可逆性即使在误差随副本数量多项式增长的层面依然存在，进一步强化了该猜想。我们还推导了非纠缠操作下指数强逆成本的半定规划下界。最后，对于完全保持PPT的操作类别，我们构造了可解析求解的反对称态族，展现出指数强逆不可逆性。值得注意的是，据我们所知，即使在更严格的LOCC操作类别下，目前也尚未发现指数强逆成本与对应的蒸馏纠缠之间存在类似分离。

英文摘要

The manipulation of quantum entanglement is fundamentally irreversible: some mixed entangled states require pure entanglement for their preparation, although no pure entanglement can be recovered from them by local operations and classical communication. This irreversibility is known to persist even under the maximal class of operations that do not generate entanglement, revealing a fundamental distinction between entanglement theory and thermodynamics. We construct cases for which any attempt to restore reversibility necessarily incurs an error that increases exponentially with the number of copies. Technically, we demonstrate a strict separation between the exponential strong-converse distillable entanglement and the exponential strong-converse entanglement cost. Our result resolves a conjecture posed by Lami and Regula (Nat. Phys. 19, 184-189 (2023)) and strengthens it by showing that the irreversibility of entanglement persists even at the level of polynomially (in the number of copies) growing error. We further derive a semidefinite-programming lower bound on the exponential strong-converse cost under non-entangling operations. Finally, for the class of completely PPT-preserving operations, we construct analytically solvable families of antisymmetric states exhibiting the exponential strong-converse irreversibility. Remarkably, to our knowledge, no analogous separation between exponential strong converse cost and the analogous distillable entanglement is currently known even under the more restrictive class of LOCC operations.

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6+16 pages