关于量子态可分性的O-约化判据

文章提出了一类纠缠目击者.它们是以局域正交可观测量的形式给出的,因而自动提供了利用局域测量和经典通信来探测纠缠的方法.利用Jamiokowski同构得到了相应的非完全正的正映射,从而导出一类新的可分性判据——O-约化判据.约化判据和重排判据都是该判据的特例.另外,还发现O-约化判据可以通过测量局域正交可观测量的一个厄米关联矩阵来获得物理的实现.作为应用,构造了Horodecki在1997年发现的第一个束缚纠缠态的纠缠目击者的清晰形式,并且提出了一类dd束缚纠缠态,其纠缠可以通过对局域正交可观测量进行置换来探测.     

Characterizing entanglement via uncertainty relations

We derive a family of necessary separability criteria for finite-dimensional systems based on inequalities for variances of observables. We show that every pure bipartite entangled state violates some of these inequalities. Furthermore, a family of bound entangled states and true multipartite entangled states can be detected. The inequalities also allow us to distinguish between different classes of true tripartite entanglement for qubits. We formulate an equivalent criterion in terms of covariance matrices. This allows us to apply criteria known from the regime of continuous variables to finite-dimensional systems.     

Bound entanglement provides convertibility of pure entangled states

I show that two distant parties can transform pure entangled states to arbitrary pure states by stochastic local operations and classical communication (SLOCC) at the single copy level, if they share bound entangled states. This is the effect of bound entanglement since this entanglement processing is impossible by SLOCC alone. A similar effect of bound entanglement exists in three qubits where two incomparable entangled states of GHZ (Greenberger, Horne, and Zeilinger) and W can be interconverted. In general, multipartite settings composed by N distant parties, all N-partite pure entangled states are interconvertible by SLOCC with the assistance of bound entangled states with positive partial transpose.     

Bound entanglement and continuous variables

We introduce the definition of generic bound entanglement for the case of continuous variables. We provide some examples of bound entangled states for that case, and discuss their physical sense in the context of quantum optics. We raise the question of whether the entanglement of these states is generic. As a by-product we obtain a new many parameter family of bound entangled states with positive partial transpose. We also point out that the "entanglement witnesses" and positive maps revealing the corresponding bound entanglement can easily be constructed.     

Comprehensive test of entanglement for two-level systems via the indeterminacy relationship

A 3-setting Bell-type inequality enforced by the indeterminacy relation of complementary local observables is proposed as an experimental test of 2-qubit entanglement. The proposed inequality has the advantage of being a sufficient and necessary criterion of separability. Therefore any entangled 2-qubit state cannot escape the detection by this kind of test. It turns out that the orientation of the local testing observables plays a crucial role in our perfect detection of entanglement.     

Covariance matrices and the separability problem

We propose a unifying approach to the separability problem using covariance matrices of locally measurable observables. From a practical point of view, our approach leads to strong entanglement criteria that allow us to detect the entanglement of many bound entangled states in higher dimensions and which are at the same time necessary and sufficient for two qubits. From a fundamental perspective, our approach leads to insights into the relations between several known entanglement criteria--such as the computable cross-norm and local uncertainty criteria--as well as their limitations.     

Bound entanglement and teleportation for arbitrary bipartite systems

We construct bound entangled states that are entangled but from which no entanglement can De olstilled It all parues are allowed only by performing local operations and classical communications. Moreover, as applications, a detailed example is presented. This example can illuminate that the fidelity of transmission using a bound entangled state is not bigger than a classical scheme.     

Collective uncertainty entanglement test

For a given pure state of a composite quantum system we analyze the product of its projections onto a set of locally orthogonal separable pure states. We derive a bound for this product analogous to the entropic uncertainty relations. For bipartite systems the bound is saturated for maximally entangled states and it allows us to construct a family of entanglement measures, we shall call collectibility. As these quantities are experimentally accessible, the approach advocated contributes to the task of experimental quantification of quantum entanglement, while for a three-qubit system it is capable to identify the genuine three-party entanglement.     

Observable estimation of bipartite mixed-state entanglement

An analytic lower bound is presented for bipartite mixed-state entanglement which is obtained from convex roof construction of a variational definition of pure-state negativity. It is shown that this lower bound can be directly measured by one single projection operator or a few local observables in experiments without the requirement of simultaneous multiple copies of states. In particular, we show that the lower bound can serve as an exact entanglement measure for isotropic states.     

Deterministic exact teleportation via two partially entangled pairs of particles

We present an explicit protocol for deterministic exact teleportation via two partially entangled pairs of particles. The protocol consists of a local generalized measurement described by a positive operator-valued measure, one-way classical communication, and a corresponding local unitary operation. We find the required generalized measurement, which can experimentally be realized by performing a unitary operation in the extended space and a conventional orthogonal measurement. A simple protocol for deterministic entanglement concentration is also obtained.     

Unextendible Product Bases,Uncompletable Product Bases and Bound Entanglement

We report new results and generalizations of our work on unextendible product bases (UPB), uncompletable product bases and bound entanglement. We present a new construction for bound entangled states based on product bases which are only completable in a locally extended Hilbert space. We introduce a very useful representation of a product basis, an orthogonality graph. Using this representation we give a complete characterization of unextendible product bases for two qutrits. We present several generalizations of UPBs to arbitrary high dimensions and multipartite systems. We present a sufficient condition for sets of orthogonal product states to be distinguishable by separable superoperators. We prove that bound entangled states cannot help increase the distillable entanglement of a state beyond its regularized entanglement of formation assisted by bound entanglement.     

Asymptotic manipulations of entanglement can exhibit genuine irreversibility

It is commonly believed that distillation of entanglement can be, in general, irreversible. Perhaps the strongest evidence is constituted by the existence of the bound entangled states. However, even a single example of state exhibiting this irreversibility has not been found so far. We show that for a family of states the process of distillation of entanglement is truly irreversible. These states have a nonzero amount of bound entanglement and, at most, a very small amount of free entanglement.     

Irreversibility for all bound entangled states

We derive a new inequality for entanglement for a mixed four-partite state. Employing this inequality, we present a one-shot lower bound for entanglement cost and prove that entanglement cost is strictly larger than zero for any entangled state. We demonstrate that irreversibility occurs in the process of formation for all nondistillable entangled states. In this way we solve a long standing problem of how "real" is entanglement of bound entangled states. Using the new inequality we also prove the impossibility of local cloning of a known entangled state.     

Entanglement witnesses and geometry of entanglement of two-qutrit states

We construct entanglement witnesses with regard to the geometric structure of the Hilbert-Schmidt space and investigate the geometry of entanglement. In particular, for a two-parameter family of two-qutrit states that are part of the magic simplex, we calculate the Hilbert-Schmidt measure of entanglement. We present a method to detect bound entanglement which is illustrated for a three-parameter family of states. In this way, we discover new regions of bound entangled states. Furthermore, we outline how to use our method to distinguish entangled from separable states.     

Asymptotic violation of Bell inequalities and distillability

A multipartite quantum state violates a Bell inequality asymptotically if, after jointly processing by general local operations an arbitrarily large number of copies of it, the result violates the inequality. In the bipartite case we show that asymptotic violation of the Clauser-Horne-Shimony-Holt inequality is equivalent to distillability. Hence, bound entangled states do not violate it. In the multipartite case we consider the complete set of full-correlation Bell inequalities with two dichotomic observables per site. We show that asymptotic violation of any of these inequalities by a multipartite state implies that pure-state entanglement can be distilled from it, although the corresponding distillation protocol may require that some of the parties join into several groups. We also obtain the extreme points of the set of distributions generated by measuring N quantum systems with two dichotomic observables per site.     

Entanglement conditions for two-mode states

We provide a class of inequalities whose violation shows the presence of entanglement in two-mode systems. We initially consider observables that are quadratic in the mode creation and annihilation operators and find conditions under which a two-mode state is entangled. Further examination allows us to formulate additional conditions for detecting entanglement. We conclude by showing how the methods used here can be extended to find entanglement in systems of more than two modes.     

Optimal entanglement criterion for mixed quantum states

We develop a strong and computationally simple entanglement criterion. The criterion is based on an elementary positive map Phi which operates on state spaces with even dimension N > or = 4. It is shown that Phi detects many entangled states with a positive partial transposition (PPT) and that it leads to a class of optimal entanglement witnesses. This implies that there are no other witnesses which can detect more entangled PPT states. The map Phi yields a systematic method for the explicit construction of high-dimensional manifolds of bound entangled states.     

Unconditional continuous variable entanglement cascading

We demonstrate that the Gaussian entanglement cascading can be realized unconditionally for any nonzero squeezing in all of the entangled sources. We obtain the upper bound of the Gaussian cascaded entanglement, which cannot be exceeded by any entanglement cascading protocol based on Gaussian local operations and classical communications. We then propose an unconditional entanglement cascading protocol that can produce the cascaded entanglement reaching the upper bound. The protocol, as a generalization of the standard continuous variable teleportation, includes two steps: (i) each repeater site locally implements the Bell measurement and classically sends the results to Bob; (ii) Bob optimally displaces his own mode based on these results.     

A subsystem-independent generalization of entanglement

We present a generalization of entanglement based on the idea that entanglement is relative to a distinguished subspace of observables rather than a distinguished subsystem decomposition. A pure quantum state is entangled relative to such a subspace if its expectations are a proper mixture of those of other states. Many information-theoretic aspects of entanglement can be extended to this observable-based setting, suggesting new ways of measuring and classifying multipartite entanglement. By going beyond the distinguishable-subsystem framework, generalized entanglement also provides novel tools for probing quantum correlations in interacting many-body systems.     

Separability criterion for quantum effects

Entanglement of quantum states is absolutely essential for modern quantum sciences and technologies. It is natural to extend the notion of entanglement to quantum observables dual to quantum states. For quantum states, various separability criteria have been proposed to determine whether a given state is entangled. In this Letter, we propose a separability criterion for specific quantum effects (binary observables) that can be regarded as a dual version of the Bell–Clauser–Horne–Shimony–Holt (Bell–CHSH) inequality for quantum states. The violation of the dual version of the Bell–CHSH inequality is confirmed by using IBM's cloud quantum computer. As a consequence, the violation of our inequality rules out the maximal tensor product state space, that satisfies information causality and local tomography. As an application, we show that an entangled observable which violates our inequality is useful for quantum teleportation.