Entanglement is a fundamental resource in quantum information processing, yet understanding its manipulation and transformation remains a challenge. Many tasks rely on highly entangled pure states, but obtaining such states is often challenging due to the presence of noise. Typically, entanglement manipulation procedures involving asymptotically many copies of a state are considered to overcome this problem. These procedures allow for distilling highly entangled pure states from noisy states, which enables a wide range of applications, such as quantum teleportation and quantum cryptography. When it comes to manipulating entangled quantum systems on a single copy level, using entangled states as catalysts can significantly broaden the range of achievable transformations. Similar to the concept of catalysis in chemistry, the entangled catalyst is returned unchanged at the end of the state manipulation procedure. Our results demonstrate that despite the apparent conceptual differences between the asymptotic and catalytic settings, they are actually strongly connected and fully equivalent for all distillable states. Our methods rely on the analysis of many-copy entanglement manipulation procedures which may establish correlations between different copies. As an important consequence, we demonstrate that using an entangled catalyst cannot enhance the asymptotic singlet distillation rate of a distillable quantum state. Our findings provide a comprehensive understanding of the capabilities and limitations of both catalytic and asymptotic state transformations of entangled states, and highlight the importance of correlations in these processes.
Quantum catalytic transformations play important roles in the transformation of quantum entangled states under local operations and classical communications (LOCC). The key problems in catalytic transformations are the existence and the bounds on the catalytic states. We present the necessary conditions of catalytic states based on a set of points given by the Schmidt coefficients of the entangled source and target states. The lower bounds on the dimensions of the catalytic states are also investigated. Moreover, we give a detailed protocol of quantum mixed state transformation under entanglem…
Equivalence of Discrete and Continuous Otto-Like Engines assisted by Catalysts: Mapping Catalytic Advantages from the Discrete to the Continuous Framework
University of Gdańsk（格但斯克大学）；Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）
Quantum entanglement of pure states is usually quantified via the entanglement entropy, the von Neumann entropy of the reduced state. Entanglement entropy is closely related to entanglement distillation, a process for converting quantum states into singlets, which can then be used for various quantum technological tasks. The relation between entanglement entropy and entanglement distillation has been known only for the asymptotic setting, and the meaning of entanglement entropy in the single-copy regime has so far remained open. Here we close this gap by considering entanglement catalysis. We …
We address fundamental limitations of quantum teleportation -- the process of transferring quantum information using classical communication and preshared entanglement. We develop a new teleportation protocol based upon the idea of using ancillary entanglement catalytically, i.e. without depleting it. This protocol is then used to show that catalytic entanglement allows for a noiseless quantum channel to be simulated with a quality that could never be achieved using only entanglement from the shared state, even for catalysts with a small dimension. On the one hand, this allows for a more faith…
We consider a general resource theory that allows the use of free resource as a catalyst. We show that the amount of `resource' contained in a given state, in the asymptotic scenario, is equal to the regularized relative entropy of resource of that state, which then yields a straightforward operational meaning to this quantity. Such an answer has been long sought for in any resource theory since the usefulness of a state in information-processing tasks is directly related to the amount of resource the state possesses in the beginning. While we need to place a few assumptions in our resource th…
Catalytic coherence transformations allow the otherwise impossible state transformations using only incoherent operations with the aid of an auxiliary system with finite coherence which is not being consumed in anyway. Here we find the necessary and sufficient conditions for the deterministic and stochastic catalytic coherence transformations between pair of pure quantum states. In particular, we show that the simultaneous decrease of a family of Rényi entropies of the diagonal parts of the states under consideration are necessary and sufficient conditions for the deterministic catalytic coher…
Catalytic channels are the only noise-robust catalytic processes
Nanyang Technological University（南洋理工大学）；Nagoya University（名古屋大学）；University of Tsukuba（筑波大学）；Aix-Marseille University（艾克斯-马赛大学）；Ulsan National Institute of Science and Technology (UNIST)（蔚山科学技术院）
Entanglement-assisted concatenated quantum codes (EACQCs), constructed by concatenating two quantum codes, are proposed. These EACQCs show several advantages over the standard concatenated quantum codes (CQCs). Several families of EACQCs that, unlike standard CQCs, can beat the nondegenerate Hamming bound for entanglement-assisted quantum error correction codes (EAQECCs) are derived. Further, a number of EACQCs with better parameters than the best known standard quantum error correction codes (QECCs) and EAQECCs are also derived. In particular, several catalytic EACQCs with better parameters t…
We show that the minimal rate of noise needed to catalytically erase the entanglement in a bipartite quantum state is given by the regularized relative entropy of entanglement. This offers a solution to the central open question raised in [Groisman, PRA 72, 032317 (2005)] and complements their main result that the minimal rate of noise needed to erase all correlations is given by the quantum mutual information. We extend our discussion to the tripartite setting where we show that an asymptotic rate of noise given by the regularized relative entropy of recovery is sufficient to catalytically tr…
Determining whether a given state can be transformed into a target state using free operations is one of the fundamental questions in the study of resources theories. Free operations in resource theories can be enhanced by allowing for a catalyst system that assists the transformation and is returned unchanged, but potentially correlated, with the target state. While this has been an active area of recent research, very little is known about the necessary properties of such catalysts. Here, we prove fundamental limits applicable to a large class of correlated catalytic transformations by showi…
Quantum steganographic protocols using degenerate and entanglement-assisted quantum codes
Poornaprajna Institute of Scientific Research（普尔纳普拉吉纳科学研究学院）；Graduate Studies, Manipal Academy of Higher Education（曼帕尔高等教育大学研究生部）；Indian Institute of Technology Jodhpur（印度理工学院焦浦尔分校）
Local unitary equivalence and entanglement of multipartite pure states
在[B]中给出了任意n比特纯量子态在局域幺正（LU）运算下等价的充要条件。Kraus Phys. Rev. Lett. 104，020504（2010）]用于确定多达五个量子比特状态的不同LU等价类。由于这种分类，发现了表征多体纠缠的新参数，并给出了它们的物理解释。此外，我们还用这种方法导出了两个n比特态（n>2）的例子，它们具有任意子系统的熵都一致的性质，但它们既不是LU等价的，也不能通过一般的局域操作和经典通信相互映射.
University of Amsterdam（阿姆斯特丹大学）；QuSoft；Charles University, Prague, Czech Republic（布拉格查理大学）；Department of Computer Science, University of Oxford（牛津大学计算机系）
While all bipartite pure entangled states are known to generate correlations violating a Bell inequality, and are therefore nonlocal, the quantitative relation between pure-state entanglement and nonlocality is poorly understood. In fact, some Bell inequalities are maximally violated by non-maximally entangled states and this phenomenon is also observed for other operational measures of nonlocality. In this work, we study a recently proposed measure of nonlocality defined as the probability that a pure state displays nonlocal correlations when subjected to random measurements. We first prove t…
We show that the dynamic resource theory of quantum entanglement can be formulated using the superchannel theory. In this formulation, we identify the separable channels and the class of free superchannels that preserve channel separability as free resources, and choose the swap channels as dynamic entanglement golden units. Our first result is that the one-shot dynamic entanglement cost of a bipartite quantum channel under the free superchannels is bounded by the standard log-robustness of channels. The one-shot distillable dynamic entanglement of a bipartite quantum channel under the free su…
University of Geneva（日内瓦大学）；Center for Theoretical Physics, Polish Academy of Sciences（波兰科学院理论物理中心）；Institute of Theoretical Physics, Jagiellonian University（雅盖隆大学理论物理研究所）；Sorbonne Université, CNRS, LIP6（索邦大学、法国国家科学研究中心、LIP6实验室）
We propose a framework to characterize entanglement with quantum discord, both asymmetric and symmetric, over state extensions. In particular, we show that the minimal Bures distance of discord over state extensions is equivalent to Bures distance of entanglement. This equivalence places quantum discord at a more primitive position than entanglement conceptually in the sense that entanglement can be interpreted as an irreducible part of discord over all state extensions. Based on this equivalence, we also offer an operational meaning of Bures distance of entanglement by connecting it to quantu…
Tsinghua University（清华大学）；Frontier Science Center for Quantum Information（量子信息前沿科学中心）；Beijing Academy of Quantum Information Sciences（北京量子信息科学研究院）；Hefei National Laboratory（合肥国家实验室）
We find that when a qubit initialized in a pure state experiences pure dephasing due to interaction with an environment, separable qubit-environment states generated during the evolution also have zero quantum discord with respect to the environment. What follows is that the set of separable states which can be reached during the evolution has zero volume and hence, such effects as sudden death of qubit-environment entanglement are very unlikely. In case of the discord with respect to the qubit, a vast majority of separable states qubit-environment is discordant, but in specific situations zer…
The Einstein equivalence principle is based on the equality of gravitational mass and inertial mass, which has led to the universality of a free-fall concept. The principle has been extremely well tested so far and has been tested with a great precision. However, all these tests and the corresponding arguments are based on a classical setup where the notion of position and velocity of the mass is associated with a classical value as opposed to the quantum entities. Here, we will provide a simple protocol based on creating large spatial superposition states in a laboratory to test the fully qua…
On the equivalence between squeezing and entanglement potential for two-mode Gaussian states
Australian National University（澳大利亚国立大学）；University of California, Los Angeles (UCLA)（加利福尼亚大学洛杉矶分校）；Agency for Science, Technology and Research (A*STAR)（科学技术研究局）；Nanyang Technological University（南洋理工大学）
