Beyond complete positivity
Beyond complete positivity
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DOI：
10.1007/s11128-015-1228-1
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发表时间：
2016-04-01
影响因子：
2.5
通讯作者：
Lidar, Daniel A.
中科院分区：
文献类型：
--
作者：
Dominy, Jason M.;Lidar, Daniel A.
我们提供了线性子系统量子动力学映射的一般和一致的公式，从最小假设集发展而来，其中主要是对通常的，不相关初始系统浴状态的限制性假设的放松。我们描述了这个公式所允许的可能性空间，即，远不局限于只有完全正（CP）映射，本质上任何-线性的，保持厄米的，保持迹的映射都可以作为一个合法的子系统动态映射从一个系统耦合到一个槽的联合酉演化中产生。为这种增加的通用性所付出的代价是在可接受的初始状态集和可允许的联合系统-单元演化集之间进行权衡。作为应用，我们给出了一个简单的非cp映射的例子，它被构造为子系统动态映射，违反了量子信息理论中的一些基本不等式，如量子数据处理不等式。
We provide a general and consistent formulation for linear subsystem quantum dynamical maps, developed from a minimal set of postulates, primary among which is a relaxation of the usual, restrictive assumption of uncorrelated initial system-bath states. We describe the space of possibilities admitted by this formulation, namely that, far from being limited to only completely positive (CP) maps, essentially any -linear, Hermiticity-preserving, trace-preserving map can arise as a legitimate subsystem dynamical map from a joint unitary evolution of a system coupled to a bath. The price paid for this added generality is a trade-off between the set of admissible initial states and the allowed set of joint system-bath unitary evolutions. As an application, we present a simple example of a non-CP map constructed as a subsystem dynamical map that violates some fundamental inequalities in quantum information theory, such as the quantum data processing inequality.