We show the enhancement of distillable key rate for quantum key distribution(QKD), by local filtering, for several bound entangled states. Through our work it becomes evident that the local filtration operations, while transforming one bound entangled state to another, have the potential to increase the utility of the new state for QKD. We demonstrate three examples of `one way distillable key rate' enhancement by local filtering and in this process, discover new bound entangled states which are key distillable.
Bound entangled states with nonzero distillable key rate
本文给出了状态具有正可重密钥率的充分条件。利用这些条件，我们证明了Horodecki等人[Phys. Rev. Lett. 94，160502（2005），quant-ph/0506203]具有非零的可压缩密钥速率，并最终得到一类新的具有正的可压缩密钥速率的束缚纠缠态，但其保密压缩ccq态的可压缩密钥速率的Devetak-Winter下界为负.
Magic can be distributed non-locally in many-body entangled states, such as the low energy states of condensed matter systems. Using the Bravyi-Kitaev magic state distillation protocol, we find that non-local magic is distillable and can improve the distillation outcome. We analyze a few explicit examples and show that spin squeezing can be used to convert non-distillable states into distillable ones. Our analysis also suggests that the conventional product input states assumed by magic distillation protocols are extremely atypical among general states with distillable magic. It further justif…
In a multipartite scenario quantum entanglement manifests its most dramatic form when the state is genuinely entangled. Such a state is more beneficial for information theoretic applications if it contains distillable entanglement in every bipartition. It is, therefore, of significant operational interest to identify subspaces of multipartite quantum systems that contain such properties apriori. In this letter, we introduce the notion of unextendible biseparable bases (UBB) that provides an adequate method to construct genuinely entangled subspaces (GES). We provide an explicit construction of…
A nice and interesting property of any pure tensor-product state is that each such state has distillable entangled states at an arbitrarily small distance $ε$ in its neighborhood. We say that such nearby states are $ε$-entangled, and we call the tensor product state in that case, a "boundary separable state", as there is entanglement at any distance from this "boundary". Here we find a huge class of separable states that also share that property mentioned above -- they all have $ε$-entangled states at any small distance in their neighborhood. Furthermore, the entanglement they have is proven t…
We look into multipartite quantum states on which quantum cryptographic protocols including quantum key distribution and quantum secret sharing can be perfectly performed, and define the quantum cryptographic resource distillable rate as the asymptotic rate at which such multipartite state can be distilled from a given multipartite state. Investigating several relations between entanglement and the rate, we show that there exists a multipartite bound entangled state whose quantum cryptographic resource distillable rate is strictly positive, that is, there exists a multipartite entangled state …
A Necessary And Sufficient Condition of Distillability with unite fidelity from Finite Copies of a Mixed State: The Most Efficient Purification Protocol
The University of Tokyo（东京大学）；RIKEN Center for Quantum Computing (RQC)（理化学研究所量子计算中心）；The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳））；International Quantum Academy（国际量子学院）；Nagoya University（名古屋大学）
Using a geometric measure of entanglement quantification based on Euclidean distance of the Hermitian matrices, we obtain the minimum distance between a bipartite bound entangled $n$- qudit density matrix and the maximally mixed state.This minimum distance for which entangled density matrices necessarily have positive partial transpose (PPT) is obtained as $\frac{1}{\sqrt{\sqrt{d^n(d^n-1)}+1}}$, which is also a lower limit for the existence of 1-distillable entangled states. The separable states necessarily lie within a minimum distance of $\frac{R}{1+d^{n-1}}$ from the Identity,where R is the…
We focus on characterizing entanglement of high dimensional bipartite states using various statistical correlators for two-qudit mixed states. The salient results obtained are as follows: (a) A scheme for determining the entanglement measure given by Negativity is explored by analytically relating it to the widely used statistical correlators viz. mutual predictability, mutual information and Pearson Correlation coefficient for different types of bipartite arbitrary dimensional mixed states. Importantly, this is demonstrated using only a pair of complementary observables pertaining to the mutu…
We derive a formal connection between quantum data hiding and quantum privacy, confirming the intuition behind the construction of bound entangled states from which secret bits can be extracted. We present three main results. First, we show how to simplify the class of private states and related states via reversible local operation and one-way communication. Second, we obtain a bound on the one-way distillable entanglement of private states in terms of restricted relative entropy measures, which is tight in many cases and shows that protocols for one-way distillation of key out of states with…
Experimental construction of a W-superposition state and its equivalence to the GHZ state under local filtration
在核磁共振量子信息处理器上实验构建了一种新的三比特纠缠W叠加态（$\rm W \bar{\rm W}$）.我们给出了一个基于测量的过滤协议的可逆本地操作（ILO），转换的$\rm W \bar{\rm W}$状态到GHZ状态，使用三个辅助量子位的寄存器。此外，我们实现了一个实验性的协议，重建的三方$\rm W \bar{\rm W}$状态的全部信息，只使用两方减少密度矩阵。最近发现的一个有趣的事实是，$\rm W \bar{\rm W}$态与ILO下的GHZ态是等价的，它实际上是由它的两方约化密度矩阵重构的，而不像GHZ态。因此，我们证明，虽然$\rm W \bar{\rm W}$状态是与GHZ状态相互转换，它存储纠缠非常不同。
Entanglement distillation, an essential quantum information processing task, refers to the conversion from multiple copies of noisy entangled states to a smaller number of highly entangled states. In this work, we study the non-asymptotic fundamental limits for entanglement distillation. We investigate the optimal tradeoff between the distillation rate, the number of prepared states, and the error tolerance. First, we derive the one-shot distillable entanglement under completely positive partial transpose preserving operations as a semidefinite program and demonstrate an exact characterization…
