We provide a method to construct entanglement criteria for arbitrary multipartite systems of discrete or continuous variables and hybrid combinations of both. While any set of local operators generates a sufficient condition for entanglement of arbitrary quantum states, a suitable set leads to a necessary and sufficient criterion for pure states. The criteria are readily implementable with existing technology and reveal entanglement that remains undetected by the respective state-of-the-art methods for discrete and continuous variables.
We derive entropic inseparability criteria for the phase space representation of quantum states. In contrast to criteria involving differential entropies of marginal phase space distributions, our criteria are based on a joint distribution known as the Husimi Q-distribution. This distribution is experimentally accessible in cold atoms, circuit QED architectures and photonic systems and bears practical advantages compared to the detection of marginals. We exemplify the strengths of our entropic approach by considering several classes of non-Gaussian states where second-order criteria fail. We s…
With a two step optimization method of entanglement witness, we analytically propose a set of necessary and sufficient entanglement criteria for four qubit symmetric Greenberger-Horne-Zeilinger (GHZ) diagonal states. The criterion set contains four criteria. Two of them are linear with density matrix elements. The other two criteria are nonlinear with density matrix elements. The criterion set has a nest structure. A proper subset of the criteria is necessary and sufficient for the entanglement of a proper subset of the states. We illustrate the nest structure of criterion set with the general…
Entanglement witnesses based on first and second moments exist in the form of spin-squeezing criteria for the detection of particle entanglement from collective measurements, and in form of modified uncertainty relations for the detection of mode entanglement or steering. By revealing a correspondence between them, we show that metrologically useful spin squeezing reveals multimode entanglement in symmetric spin states that are distributed into addressable modes. We further derive tight state-independent multipartite entanglement bounds on the spin-squeezing coefficient and point out their con…
Quantitative characterization of different entanglement detection criteria for bipartite systems is presented. We review the implication sequence of these criteria and then numerically estimate volume ratios between criteria non-violating quantum states and all quantum states. The numerical approach is based on the hit-and-run algorithm, which is applied to the convex set of all quantum states embedded into a Euclidean vector space of the Hilbert-Schmidt inner product. We demonstrate that reduction, majorization, and the Rényi-entropy-based criteria are very ineffective compared to the positiv…
It is known that the partial entanglement/separability violates distributive rules with respect to the operations of taking convex hull and intersection. In this note, we give criteria for three qubit partially entangled states arising from distributive rules, together with the corresponding witnesses. The criteria will be given in terms of diagonal and anti-diagonal entries. They actually characterize those partial entanglement completely when all the entries are zero except for diagonal and anti-diagonal entries. Important states like Greenberger-Horne-Zeilinger diagonal states fall down in …
We revisit the genuine multipartite entanglement by a simplified method, which only involves the Schmidt decomposition and local unitary transformation. We construct a local unitary equivalent class of the tri-qubit quantum state, then use the trace norm of the whole correlation tensor as a measurement to detect genuine multipartite entanglement. By detailed examples, we show our result can detect more genuinely entangled states. Furthermore, we generalize the genuine multipartite entanglement criterion to tripartite higher-dimensional systems.
We propose entanglement criteria for multipartite systems via symmetric informationally complete (SIC) measurement and general symmetric informationally complete (GSIC) measurement. We apply these criteria to detect entanglement of multipartite states, such as the convex of Bell states, entangled states mixed with white noise. It is shown that these criteria are stronger than some existing ones.
Entanglement, quantum steering and nonlocality are distinct quantum correlations which are the resources behind various of quantum information and quantum computation applications. However, a central question of determining the precise quantitative relation among them is still unresolved. Here, we present a mapping criterion between Bell nonlocality and quantum steering in bipartite qudit-qubit system, as well as a mapping criterion between quantum steering and quantum entanglement in bipartite qubit-qudit system, starting from the fundamental concepts of quantum correlations. Precise quantita…
We use quantum entanglement witnesses derived from Gaussian operators to study the separable criteria of continuous variable states. We transform the validity of a Gaussian witness to a Bosonic Gaussian channel problem. It follows that the maximal means of two-mode and some four-mode Gaussian operators over product pure states are achieved by vacuum (or coherent states and squeezed states) according to the properties of Bosonic Gaussian channels. Then we have necessary and sufficient criteria of separability not only for Gaussian quantum states, but also for non-Gaussian states prepared by pho…
Entanglement, EPR steering, and Bell-nonlocality criteria for multipartite higher-spin systems
我们开发的标准，以检测三类非局域性，已被证明由怀斯曼等人。[物理评论快报。98，140402（2007）]是不等价的：纠缠，EPR转向，和本地隐藏变量理论的失败。我们使用Cavalcanti等人的方法[Phys. Rev. Lett. 99，210405（2007）]的连续变量，以开发非定域性标准的任意自旋观测定义在离散希尔伯特空间。因此，该标准适用于多站点量子，即，系统的固定尺寸d，并采取不等式的形式。我们发现，当量子点数目N足够大时，优化的高关联非最大纠缠态在任意d下都可以违反检验局域隐变量的自旋矩不等式（贝尔不等式）.另一方面，纠缠的自旋不等式被违反，从而检测纠缠的状态，为任意的d和N，并与违反，增加与N.我们表明，一个时刻纠缠不等式可以检测任意广义多体格林伯格-霍恩-蔡林格状态的纠缠。因为它们涉及原子系统的自然观测量，所以相关的自旋算符关联应该在被囚禁的超冷原子气体和离子阱中容易观察到。
Physical transformations are described by linear maps that are completely positive and trace preserving (CPTP). However, maps that are positive (P) but not completely positive (CP) are instrumental to derive separability/entanglement criteria. Moreover, the properties of such maps can be linked to entanglement properties of the states they detect. Here, we extend the results presented in [Phys. Rev A 93, 042335 (2016)], where sufficient separability criteria for bipartite systems were derived. In particular, we analyze the entanglement depth of an $N$-qubit system by proposing linear maps that…
Entanglement detection is essential in quantum information science and quantum many-body physics. It has been proved that entanglement exists almost surely for a random quantum state, while the realizations of effective entanglement criteria usually consume exponential resources, and efficient criteria often perform poorly without prior knowledge. This fact implies a fundamental limitation might exist in the detectability of entanglement. In this work, we formalize this limitation as a fundamental trade-off between the efficiency and effectiveness of entanglement criteria via a systematic meth…
We propose an entanglement criterion, specially designed for mixed states, based on uncertainty relation and the Wigner-Yanase skew information. The variances in this uncertainty relation does not involve any classical mixing uncertainty, and thus turns out to be purely of quantum mechanical nature. We show that any mixed entangled state can be characterized by our criterion. We demonstrate its utility for several generalized mixed entangled state including Werner states and it turns out to be stronger than any other known criterion in identifying the correct domain of relevant parameters for …
