固定量子系统上的每一个足够丰富的测量集合通过最佳偏差定义了该系统状态的统计范数，该最佳偏差可以在使用来自该集合的测量区分状态时实现（假设相等的先验）。Holevo-Helstrom定理说，对于所有测量的集合，这个范数是迹范数。对于有限维，任何范数的下限和上限都是由迹范数的常数（尽管依赖于维数）的倍数来限定的，因此我们为自己设定了计算或限定最佳可能的“支配常数”的任务，这些常数对应于各种受限的测量集合，从而确定这些集合相对于所有测量集合的最坏情况和最好情况性能。我们看看的情况下，允许的集合由一个单一的测量，即均匀随机连续POVM及其近似2-设计和4-设计分别。在这里，我们发现渐近紧的优势常数的界限。此外，我们分析了多方设置与任何LOCC测量允许。在两个当事人的情况下，我们表明，较低的控制常数是相同的张量积的局部均匀随机POVMs（常数）。这肯定地回答了一个关于二分数据隐藏的（接近）最优性的公开问题：LOCC在区分d x d二分系统的两个正交状态时可以实现的偏差是Omega（1/d），这是已知的紧。最后，我们使用我们的分析，以获得任何这样的测量的确定性关系（在桑切斯-鲁伊斯的意义上）和下界的局部可访问的信息的二分系统。
英文摘要：
Every sufficiently rich set of measurements on a fixed quantum system defines a statistical norm on the states of that system via the optimal bias that can be achieved in distinguishing the states using measurements from that set (assuming equal priors). The Holevo-Helstrom theorem says that for the set of all measurements this norm is the trace norm. For finite dimension any norm is lower and upper bounded by constant (though dimension dependent) multiples of the trace norm, so we set ourselves the task of computing or bounding the best possible "constants of domination" for the norms corresponding to various restricted sets of measurements, thereby determining the worst case and best case performance of these sets relative to the set of all measurements.
We look at the case where the allowed set consists of a single measurement, namely the uniformly random continuous POVM and its approximations by 2-designs and 4-designs respectively. Here we find asymptotically tight bounds for the constants of domination.
Furthermore, we analyse the multipartite setting with any LOCC measurement allowed. In the case of two parties, we show that the lower domination constant is the same as that of a tensor product of local uniformly random POVMs (up to a constant). This answers in the affirmative an open question about the (near-)optimality of bipartite data hiding: The bias that can be achieved by LOCC in discriminating two orthogonal states of a d x d bipartite system is Omega(1/d), which is known to be tight. Finally, we use our analysis to derive certainty relations (in the sense of Sanchez-Ruiz) for any such measurements and to lower bound the locally accessible information for bipartite systems.
Global versus Local Discrimination of Locally Implementable Multipartite Unitaries
Indian Institute of Science Education and Research Thiruvananthapuram（印度科学教育研究所特里凡得琅分校）；Indian Institute of Technology Bhubaneswar（印度技术学院布巴内斯瓦尔分校）；S. N. Bose National Centre for Basic Sciences（S.N. 玻色基础科学国家中心）
Tight Universal Bounds on Quantum Data Hiding with Multipartite Werner States
Central High School（中央高中）；Department of Mathematics, University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校数学系）；Department of Physics, University of Rhode Island（罗德岛大学物理系）
Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China（电子科技大学前沿科学技术研究院）；International Iberian Nanotechnology Laboratory（国际伊比利亚纳米技术实验室）；Department of Physics, Shiv Nadar Institution of Eminence（锡夫纳达尔卓越学院物理系）
