Absolutely Maximally Entangled (AME) states are maximally entangled for every bipartition of the system. They are crucial resources for various quantum information protocols. We present techniques for verifying either two AME states are equivalent concerning Stochastic Local Operations and Classical Communication (SLOCC). The conjecture that for a given multipartite quantum system all AME states are SLOCC-equivalent is falsified. We also show that the existence of AME states with minimal support of 6 or more particles results in the existence of infinitely many such non-SLOCC-equivalent states. Moreover, we present AME states which are not SLOCC-equivalent to the existing AME states with minimal support.

中文翻译：

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具有绝对最大纠缠态的经典通信的随机局部操作

对于系统的每个划分，绝对最大纠缠（AME）状态都是最大纠缠。它们是各种量子信息协议的关键资源。我们提出了用于验证关于随机本地操作和经典通信（SLOCC）的两个AME状态是否等效的技术。对于给定的多部分量子系统，所有AME状态都等于SLOCC的猜想被证伪了。我们还表明，具有最少6个或更多粒子支持的AME状态的存在导致无限多个此类非SLOCC等效状态的存在。此外，我们以最小的支持提出了与SAME不等效的AME状态。