There is an ongoing effort to quantify entanglement of quantum pure states for systems with more than two subsystems. We consider three approaches to this problem for three-qubit states: choosing a basis which puts the state into a standard form, enumerating ``local invariants,'' and using operational quantities such as the number of maximally entangled states which can be distilled. In this paper we evaluate a particular standard form, the {\it Schmidt form}, which is a generalization of the Schmidt decomposition for bipartite pure states. We show how the coefficients in this case can be parametrized in terms of five physically meaningful local invariants; we use this form to prove the efficacy of a particular distillation technique for GHZ triplets; and we relate the yield of GHZs to classes of states with unusual entanglement properties, showing that these states represent extremes of distillability as functions of two local invariants.
Genuineness and distillability of entanglement play a key role in quantum information tasks, and they are easily disturbed by the noise. We construct a family of multipartite states without genuine entanglement and distillability sudden death across every bipartition, respectively. They are realized by establishing the noise as the multipartite high dimensional Pauli channels. Further, we construct a locally unitary channel as another noise such that the multipartite Greenberger-Horne-Zeilinger state becomes the D{ü}r's multipartite state. We also show that the quantum information masking stil…
When a quantum system is distributed to spatially separated parties, it is natural to consider how the system evolves when the parties perform local quantum operations with classical communication (LOCC). However, the structure of LOCC channels is exceedingly complex leaving many important physical problems unsolved. In this paper we consider generalized resource theories of entanglement based on different relaxations to the class of LOCC. The behavior of various entanglement measures is studied under non-entangling channels, as well as the newly introduced classes of dually non-entangling and…
我们考虑了非正部分转置（NPT）束缚纠缠态的存在性问题。正如我们所知，这种状态的存在特别意味着可纠缠的不可加性。此外，它还排除了对一组可解释状态的简单数学描述。可蒸馏性等价于对于某个n的所谓的n拷贝可蒸馏性。我们考虑一个特定的状态，已知是1-副本不可分割的，这是应该是绑定纠缠。我们研究了它的两拷贝可重叠性问题，归结为某些投影Q与Schmidt秩二态的最大重叠不超过1/2。这种财产我们称之为半财产。我们首先表明，最大的重叠可以达到的向量，不是简单的产品形式，相对于两个副本之间的削减。然后，我们攻击的问题，在两个方面：a）证明了半性质的施密特秩二状态的一些类b）限制所需的重叠从上面的所有施密特秩二状态。我们已经成功地证明了半性质的广泛类的状态，并限制重叠从上述c<3/4。此外，我们将该问题转化为以下矩阵分析问题：将矩阵A \otimes I + I \otimes B的两个最大奇异值的平方和与A，B的无痕4 × 4矩阵绑定，并且Tr A^ \dagger A + Tr B^ \dagger B = 1/4。
Two-copy distillability of one-copy-undistillable negative-partial-transpose states in every dimension
Hon Hai (Foxconn) Research Institute（鸿海（富士康）研究院）；Department of Physics and Center for Quantum Frontiers of Research & Technology (QFort), National Cheng Kung University（国立成功大学物理系与量子前沿研究与技术中心 (QFort)）
The pure entangled state is of vital importance in the field of quantum information. The process of asymptotically extracting pure entangled states from many copies of mixed states via local operations and classical communication is called entanglement distillation. The entanglement distillability problem, which is a long-standing open problem, asks whether such process exists. The 2-copy undistillability of $4\times4$ undistillable Werner states has been reduced to the validness of the a matrix inequality, that is, the sum of the squares of the largest two singular values of matrix $A\otimes …
We discuss the relation between entanglement and nonlocality in the hidden nonlocality scenario. Hidden nonlocality signifies nonlocality that can be activated by applying local filters to a particular state that admits a local hidden-variable model in the Bell scenario. We present a fully-biseparable three-qubit bound entangled state with a local model for the most general (non-sequential) measurements. This proves for the first time that bound entangled states can admit a local model for general measurements. We furthermore show that the local model breaks down when suitable local filters ar…
Quantum computing is among the most far-reaching technologies of the 21st century, tackling challenges at the cutting edge of physics. This new paradigm in computer science harnesses quantum entanglement, one striking non-intuitive feature of quantum mechanics and a cornerstone of quantum information, to provide computation with a quantum speed-up over the best-known classical algorithms and to enable encrypted data communication against eavesdropping. The bulk of this article is focused on providing a deep and abiding understanding of non-relativistic matrix mechanics by demonstrating the fun…
Decoherence Mitigation with Local NOT Gates in Multipartite Systems
Qdit Labs Pvt. Ltd.（Qdit Labs有限公司）；Indian Institute of Technology Hyderabad（印度理工学院海德拉巴分校）；Poornaprajna Institute of Scientific Research（普尔纳普拉贾科学研究学院）；University of Calgary（卡尔加里大学）
We exploit insights into the geometry of bosonic and fermionic Gaussian states to develop an efficient local optimization algorithm to extremize arbitrary functions on these families of states. The method is based on notions of gradient descent attuned to the local geometry which also allows for the implementation of local constraints. The natural group action of the symplectic and orthogonal group enables us to compute the geometric gradient efficiently. While our parametrization of states is based on covariance matrices and linear complex structures, we provide compact formulas to easily con…
Optimal entanglement criteria from trace invariants
S. N. Bose National Centre for Basic Sciences（S.N. 玻色基础科学国家中心）；Indian Statistical Institute（印度统计研究所）；Université de Toulouse（图卢兹大学）；Laboratoire de Physique Théorique, Université de Toulouse, CNRS, UPS（理论物理实验室，图卢兹大学，法国国家科学研究中心）
Let $Γ(\mathcal{H})$ be the boson Fock space over a finite dimensional Hilbert space $\mathcal{H}$. It is shown that every gaussian symmetry admits a Klauder-Bargmann integral representation in terms of coherent states. Furthermore, gaussian symmetries, gaussian states and second quantization contractions, all of these operators belong to a weakly closed, selfadjoint semigroup $\mathcal{E}_2(\mathcal{H})$ of bounded operators in $Γ(\mathcal{H})$. This yields, a new parametrization of gaussian states, which is a very fruitful alternative to the customary parametrization by position-momentum mea…
Five-Dimensional Compatibility and Stratified Local-Unitary Structure of Pure Three-Qubit States
School of Physics and Materials Engineering, Hefei Normal University（合肥师范学院物理与材料工程学院）；School of Physics, Anhui University（安徽大学物理学院）；Leibniz International Joint Research Center of Materials Sciences of Anhui Province, Anhui University（安徽大学安徽省材料科学 Leibniz 国际联合研究中心）
A unitary coupled-cluster (UCC) form for the wavefunction in the variational quantum eigensolver has been suggested as a systematic way to go beyond the mean-field approximation and include electron correlation in solving quantum chemistry problems on a quantum computer. Although being exact in the limit of including all possible coupled-cluster excitations, practically, the accuracy of this approach depends on how many and what kind of terms are included in the wavefunction parametrization. Another difficulty of UCC is a growth of the number of simultaneously entangled qubits even at the fixe…
