Monotones and invariants for multi-particle quantum states
Monotones and invariants for multi-particle quantum states
复制标题
DOI：
10.1088/0305-4470/34/35/305
复制
发表时间：
2001-03
期刊：
影响因子：
--
通讯作者：
H. Barnum;N. Linden
中科院分区：
文献类型：
--
作者：
H. Barnum;N. Linden
我们引入了新的纠缠单调量，它将那些基于优超对二分态纠缠进行偏序排列的情况推广到了多方情形。我们给出了一些例子，说明它们对通过局域操作和经典通信在多体态之间进行确定性和概率性转换所施加的限制。这些限制包括那些并非由任何二分态考虑所产生的限制。当各方共享多个态时，我们推导出了每个态的单调量与集体处理的单调量之间的超乘性关系。我们还研究了局域幺正变换下的多项式不变量，并表明这类不变量中的很大一部分在集体幺正处理下是不变的，并且是可乘的，例如，这对一个态的多个副本到另一个态的多个副本的精确转换施加了限制。
We introduce new entanglement monotones which generalize, to the case of many parties, those which give rise to the majorization-based partial ordering of bipartite states' entanglement. We give some examples of restrictions they impose on deterministic and probabilistic conversion between multipartite states via local actions and classical communication. These include restrictions which do not follow from any bipartite considerations. We derive supermultiplicativity relations between each state's monotones and the monotones for collective processing when the parties share several states. We also investigate polynomial invariants under local unitary transformations, and show that a large class of these are invariant under collective unitary processing and also multiplicative, putting restrictions, for example, on the exact conversion of multiple copies of one state to multiple copies of another.