We introduce a reversible theory of exact entanglement manipulation by establishing a necessary and sufficient condition for state transfer under trace-preserving transformations that completely preserve the positivity of partial transpose (PPT). Under these free transformations, we show that logarithmic negativity emerges as the pivotal entanglement measure for determining entangled states' transformations, analogous to the role of entropy in the second law of thermodynamics. Previous results have proven that entanglement is irreversible under quantum operations that completely preserve PPT and leave open the question of reversibility for quantum operations that do not generate entanglement asymptotically. However, we find that going beyond the complete positivity constraint imposed by standard quantum mechanics enables a reversible theory of exact entanglement manipulation, which may suggest a potential incompatibility between the reversibility of entanglement and the fundamental principles of quantum mechanics.

翻译：我们通过建立完全保持部分转置正性（PPT）的迹保持变换下态转移的充分必要条件，引入了一种精确纠缠操控的可逆理论。在这些自由变换下，我们证明对数负性成为决定纠缠态变换的关键纠缠度量，类似于热力学第二定律中熵的作用。先前的结果已证明，在完全保持PPT的量子操作下纠缠是不可逆的，并且对于渐近状态下不产生纠缠的量子操作，其可逆性问题悬而未决。然而，我们发现超越标准量子力学所施加的完全正性约束，能够实现精确纠缠操控的可逆理论，这可能表明纠缠的可逆性与量子力学基本原理之间存在潜在的不兼容性。