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.     

Thermal entanglement in two qutrits system

The thermal entanglement in a two-qutrit system with two spins coupled by exchange interaction is investigated in terms of the measure of entanglement called negativity. It is found that the thermal entanglement is present and evolvements symmetrically between both ferromagnetic and antiferromagnetic exchange couplings with the temperature. Moreover the critical temperature at which the negativity vanishes increases with the exchange coupling constant J. From the temperature and magnetic field dependences we demonstrate that the temperature and the magnetic field can affect the feature of the thermal entanglement significantly.     

Recovery of entanglement lost in entanglement manipulation

When an entangled state is transformed into another one with probability one by local operations and classical communication, the quantity of entanglement decreases. This Letter shows that entanglement lost in the manipulation can be partially recovered by an auxiliary entangled pair. As an application, a maximally entangled pair can be obtained from two partially entangled pairs with probability one. Finally, this recovery scheme reveals a fundamental property of entanglement relevant to the existence of incomparable states.     

Detecting entanglement using a double-quantum-dot turnstile

We propose a scheme based on using the singlet ground state of an electron spin pair in a double-quantum-dot nanostructure as a suitable setup for detecting entanglement between electron spins via the measurement of an optimal entanglement witness. Using time-dependent gate voltages and magnetic fields the entangled spins are separated and coherently rotated in the quantum dots and subsequently detected at spin-polarized quantum point contacts. We analyze the coherent time evolution of the entangled pair and show that by counting coincidences in the four exits an entanglement test can be done. This setup is close to present-day experimental possibilities and can be used to produce pairs of entangled electrons "on demand."     

Polarization entanglement purification using spatial entanglement

We present a scheme for entanglement purification with linear optics that works for currently available parametric down-conversion sources, in contrast to a previous scheme [J. W. Pan, Nature (London) 410, 1067 (2001)]] that relied on ideal single-pair sources. The present scheme makes use of spatial entanglement in order to purify polarization entanglement. Surprisingly, spatial entanglement as an additional resource also leads to a substantial improvement in entanglement output compared to the previous scheme.     

Taming multiparticle entanglement

We present an approach to characterize genuine multiparticle entanglement by using appropriate approximations in the space of quantum states. This leads to a criterion for entanglement which can easily be calculated by using semidefinite programing and improves all existing approaches significantly. Experimentally, it can also be evaluated when only some observables are measured. Furthermore, it results in a computable entanglement monotone for genuine multiparticle entanglement. Based on this, we develop an analytical approach for the entanglement detection in cluster states, leading to an exponential improvement compared with existing schemes.     

Measuring quantum entanglement without prior state reconstruction

It is shown that, despite strong nonlinearity, entanglement of formation of a two-qubit state can be measured without prior state reconstruction. Collective measurements on a small number of copies are provided that allow one to determine quantum concurrence via estimation of only four parameters. It is also pointed out that another entanglement measure based on so-called "negativity" can also be measured in a similar way. The result is related to the general problem: What kind of information can be extracted efficiently from an unknown quantum state?     

光学体系宏观-微观纠缠及其在量子密钥分配中的应用

宏观-微观纠缠最早起源于“薛定谔的猫”思想实验, 是指在宏观体系与微观体系之间建立量子纠缠. 实现宏观-微观纠缠可以利用多种物理体系来完成, 本文重点介绍了在光学体系中制备和检验宏观-微观纠缠的发展过程. 从最初的受激辐射单光子量子克隆到光学参量放大, 再到相空间的位移操作, 实验上制备宏观-微观纠缠的方法取得了长足的进步. 利用非线性光学参量放大过程制备的宏观-微观纠缠的光子数可以达到10⁴量级, 人眼已经可以观察到, 因此使用人眼作为探测器来检验宏观-微观纠缠的实验开始出现. 但随后人们意识到, 粗精度的光子数探测器, 例如人眼, 无法严格判定宏观-微观纠缠的存在. 为了解决这个难题, 提出了一种巧妙的方法, 即在制备宏-微观纠缠后, 利用局域操作过程将宏观态再变为微观态, 通过判定微观纠缠存在的方法来判定宏微观纠缠的存在. 之后相空间的位移操作方法将宏观态的粒子数提高到10⁸, 并且实现了纠缠的严格检验. 利用光机械实现宏观-微观纠缠的方案也被提出. 由于量子密钥分配中纠缠是必要条件, 而宏观-微观纠缠态光子数较多这一优势可能会对量子密钥分配的传输距离有所提高. 本文介绍了利用相位纠缠的相干态来进行量子秘钥分配的方案, 探讨了利用宏观-微观纠缠实现量子密钥分配的可能性.     

Covariant holographic entanglement negativity

We propose a covariant holographic conjecture for the entanglement negativity of bipartite mixed states in \((1+1)\)-dimensional conformal field theories dual to bulk non static \(AdS_{3}\) configurations. Application of our conjecture to \((1+1)\)-dimensional conformal field theories dual to bulk non extremal and extremal rotating BTZ black holes exactly reproduce the corresponding entanglement negativity obtained through the replica technique, in the large central charge limit. We briefly discuss the issue of the generalization of our conjecture to higher dimensions.     

Macroscopic entanglement by entanglement swapping

We present a scheme for entangling two micromechanical oscillators. The scheme exploits the quantum effects of radiation pressure and it is based on a novel application of entanglement swapping, where standard optical measurements are used to generate purely mechanical entanglement. The scheme is presented by first solving the general problem of entanglement swapping between arbitrary bipartite Gaussian states, for which simple input-output formulas are provided.     

Topological estimator of block entanglement for Heisenberg antiferromagnets

We introduce a computable estimator of block entanglement entropy for many-body spin systems admitting total singlet ground states. Building on a simple geometrical interpretation of entanglement entropy of the so-called valence bond states, this estimator is defined as the average number of common singlets to two subsystems of spins. We show that our estimator possesses the characteristic scaling properties of the block entanglement entropy in critical and noncritical one-dimensional Heisenberg systems. We invoke this new measure to examine entanglement scaling in the two-dimensional Heisenberg model on a square lattice revealing an "area law" for the gapped phase and a logarithmic correction to this law in the gapless phase.     

Modular entanglement

We introduce and discuss the concept of modular entanglement. This is the entanglement that is established between the end points of modular systems composed by sets of interacting moduli of arbitrarily fixed size. We show that end-to-end modular entanglement scales in the thermodynamic limit and rapidly saturates with the number of constituent moduli. We clarify the mechanisms underlying the onset of entanglement between distant and noninteracting quantum systems and its optimization for applications to quantum repeaters and entanglement distribution and sharing.     

Anti-symmetry consideration on the preservation of entanglement of spin system

In this work we offer an approach to protect the entanglement based on the anti-symmetric property of the Hamiltonian. Our main objective is to protect the entanglement of a given initial three-qubit state which is governed by Hamiltonian of a three-spin Ising chain in site-dependent transverse fields. We show that according to anti-symmetric property of the Hamiltonian with respect to some operators mimicking the time reversal operator, the dynamics of the system can be effectively reversed. It equips us to control the dynamics of the system. The control procedure is implemented as a sequence of cyclic evolution; accordingly the entanglement of the system is protected for any given initial state with any desired accuracy and long-time. Using this approach we could control not only the multiparty entanglement but also the pairwise entanglement. It is also notable that in this paper although we restrict ourselves mostly within a three-spin Ising chain in site-dependent transverse fields, our approach could be applicable to any n$n$-qubit spin system models.     

Quantum entanglement in nitrosyl iron complexes

Recent magnetic susceptibility measurements for polycrystalline samples of binuclear nitrosyl iron complexes, [Fe₂(C₃H₃N₂S)₂(NO)₄] (I) and [Fe₂(SC₃H₅N₂)₂(NO)₄] (II), suggest that quantum-mechanical entanglement of the spin degrees of freedom exists in these compounds. Entanglement E exists below the temperature T _E that we have estimated for complexes I and II to be 80–90 and 110–120 K, respectively. Using an expression of entanglement in terms of magnetic susceptibility for a Heisenberg dimer, we find the temperature dependence of the entanglement for complex II. Having arisen at the temperature T _E , the entanglement increases monotonically with decreasing temperature and reaches 90–95% in this complex at T = 25 K, when the side effects are still small.     

Harmonic entanglement with second-order nonlinearity

We investigate the second-order nonlinear interaction as a means to generate entanglement between fields of differing wavelengths and show that perfect entanglement can, in principle, be produced between the fundamental and second-harmonic fields in these processes. Neither pure second-harmonic generation nor parametric oscillation optimally produce entanglement; such optimal entanglement is rather produced by an intermediate process.     

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.     

Minimizing the loss of entanglement under dimensional reduction

We investigate the possibility of transforming, under local operations and classical communication, a general bipartite quantum state on a d_A x d_B tensor-product space into a final state in 2 x 2 dimensions, while maintaining as much entanglement as possible. For pure states, we prove that Nielsens theorem provides the optimal protocol, and we present quantitative results on the degree of entanglement before and after the dimensional reduction. For mixed states, we identify a protocol that we argue is optimal for isotropic and Werner states. In the literature, it has been conjectured that some Werner states are bound entangled and in support of this conjecture our protocol gives final states without entanglement for this class of states. For all other entangled Werner states and for all entangled isotropic states some degree of free entanglement is maintained. In this sense, our protocol may be used to discriminate between bound and free entanglement.Received: 21 January 2004, Published online: 2 March 2004PACS: 03.67.Mn Entanglement production, characterization, and manipulation - 42.50.Dv Nonclassical states of the electromagnetic field, including entangled photon states; quantum state engineering and measurements - 03.65.Ud Entanglement and quantum nonlocality (e.g. EPR paradox, Bells inequalities, GHZ states, etc.)     

Locking entanglement with a single qubit

We study the loss of entanglement of a bipartite state subjected to discarding or measurement of one qubit. Examining behavior of different entanglement measures, we find that entanglement of formation, entanglement cost, logarithmic negativity, and one-way distillable entanglement are lockable measures in that they can decrease arbitrarily after measuring one qubit. We prove that any convex and asymptotically noncontinuous measure is lockable. As a consequence, all the convex-roof measures can be locked. The relative entropy of entanglement is shown to be a nonlockable measure.