We consider bipartite quantum state discrimination and present a quantum data-hiding scheme utilizing an orthogonal separable state ensemble. Using a bound on local minimum-error discrimination, we provide a sufficient condition for the separable state ensemble to be used in constructing a quantum data-hiding scheme. Our results are illustrated with various examples in bipartite quantum systems. As our scheme employs separable states of low-dimensional quantum systems, it becomes more feasible for practical implementation.
We address perfect discrimination of two separable states. When available states are restricted to separable states, we can theoretically consider a larger class of measurements than the class of measurements allowed in quantum theory. The framework composed of the class of separable states and the above extended class of measurements is a typical example of general probabilistic theories. In this framework, we give a necessary and sufficient condition to discriminate two separable pure states perfectly. In particular, we derive measurements explicitly to discriminate two separable pure states…
The phenomenon of nonlocality without entanglement(NLWE) arises in discriminating multi-party quantum separable states. Recently, it has been found that the post-measurement information about the prepared subensemble can lock or unlock NLWE in minimum-error discrimination of non-orthogonal separable states. Thus, it is natural to ask whether the availability of the post-measurement information can influence on the occurrence of NLWE even in other state-discrimination strategies. Here, we show that the post-measurement information can be used to lock as well as unlock the occurrence of NLWE in …
Distinguishability of Quantum States by Separable Operations
利用可分操作研究了多体量子态的可分性。我们首先给出了有限个正交量子态集合可通过可分操作区分的充分必要条件。这个条件的解析版本推导出的情况下，$(D-1)$纯态，其中$D$是考虑中的状态空间的总尺寸。这个结果的一些有趣的后果，然后仔细研究。值得注意的是，我们发现存在一个大类的$2\otimes 2$可分离的操作不被实现的本地操作和经典的通信。在我们的工作之前，只有一类$3\otimes 3$非局部可分运算是已知的[Bennett et al，Phys. Rev. A \textbf{59}，1070（1999）]。我们还证明了多体纯态的正交补的任何基都不能用可分操作区分当且仅当这个态不能是1或2个正交乘积态的叠加，即，的正交Schmidt数不小于3，从而推广了最近关于不可区分二部子空间的工作[Watrous，Phys.Rev.Lett. \textbf{95}，080505（2005）]。值得注意的是，我们通过考虑由两个qutrits组成的复合量子系统，得到了7维（或6维）不可区分子空间的显式构造。三个量子比特），这比先前已知的具有8维的不可区分的二分子空间稍好。
Distinguishability of quantum states under restricted families of measurements with an application to quantum data hiding
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。
A set of multipartite orthogonal quantum states is strongly nonlocal if it is locally irreducible for every bipartition of the subsystems [Phys. Rev. Lett. 122, 040403 (2019)]. Although this property has been shown in three-, four- and five-partite systems, the existence of strongly nonlocal sets in $N$-partite systems remains unknown when $N\geq 6$. In this paper, we successfully show that a strongly nonlocal set of orthogonal entangled states exists in $(\mathbb{C}^d)^{\otimes N}$ for all $N\geq 3$ and $d\geq 2$, which for the first time reveals the strong quantum nonlocality in general $N$-…
Suppose we want to benchmark a quantum device held by a remote party, e.g. by testing its ability to carry out challenging quantum measurements outside of a free set of measurements $\mathcal{M}$. A very simple way to do so is to set up a binary state discrimination task that cannot be solved efficiently by means of free measurements. If one can find pairs of orthogonal states that become arbitrarily indistinguishable under measurements in $\mathcal{M}$, in the sense that the error probability in discrimination approaches that of a random guess, one says that there is data hiding against $\mat…
For any pair of quantum states (the hypotheses), the task of binary quantum hypotheses testing is to derive the tradeoff relation between the probability $p_{01}$ of rejecting the null hypothesis and $p_{10}$ of accepting the alternative hypothesis. The case when both hypotheses are explicitly given was solved in the pioneering work by Helstrom. Here, instead, for any given null hypothesis as a pure state, we consider the worst-case alternative hypothesis that maximizes $p_{10}$ under a constraint on the distinguishability of such hypotheses. Additionally, we restrict the optimization to separ…
Nonlocality without entanglement(NLWE) is a nonlocal phenomenon that occurs in quantum state discrimination of multipartite separable states. In the discrimination of orthogonal separable states, the term NLWE is used when the quantum states cannot be discriminated perfectly by local operations and classical communication. In this case, the occurrence of NLWE is independent of nonzero prior probabilities of quantum states being prepared. Recently, it has been found that the occurrence of NLWE can depend on nonzero prior probabilities in minimum-error discrimination of nonorthogonal separable s…
Quantum nonlocality without entanglement is a fantastic phenomenon in quantum theory. This kind of quantum nonlocality is based on the task of local discrimination of quantum states. Recently, Bandyopadhyay and Halder [Phys. Rev. A 104, L050201 (2021)] studied the problem: is there any set of orthogonal states which can be locally distinguishable, but under some orthogonality preserving local measurement, each outcome will lead to a locally indistinguishable set. We say that the set with such property has hidden nonlocality. Moreover, if such phenomenon can not arise from discarding subsystems…
