Aspects of Generic Entanglement

We study entanglement and other correlation properties of random states in high-dimensional bipartite systems. These correlations are quantified by parameters that are subject to the ``concentration of measure' phenomenon, meaning that on a large-probability set these parameters are close to their expectation. For the entropy of entanglement, this has the counterintuitive consequence that there exist large subspaces in which all pure states are close to maximally entangled. This, in turn, implies the existence of mixed states with entanglement of formation near that of a maximally entangled state, but with negligible quantum mutual information and, therefore, negligible distillable entanglement, secret key, and common randomness. It also implies a very strong locking effect for the entanglement of formation: its value can jump from maximal to near zero by tracing over a number of qubits negligible compared to the size of the total system. Furthermore, such properties are generic. Similar phenomena are observed for random multiparty states, leading us to speculate on the possibility that the theory of entanglement is much simplified when restricted to asymptotically generic states. Further consequences of our results include a complete derandomization of the protocol for universal superdense coding of quantum states.     

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.     

Transformation relation between coherence and entanglement for two-qubit states

Entanglement and coherence are two important resources in quantum information theory. A question naturally arises: Is there some connection between them? We prove that the entanglement of formation and the first-order coherence of two-qubit states satisfy an inequality relation. Two-qubit pure state reaches the upper bound of this inequality. A large number of randomly generated states are used to intuitively verify the complementarity between the entanglement of formation and the first-order coherence. We give the maximum accessible coherence of two-qubit states. Our research results will provide a reliable theoretical basis for conversion of the two quantum resources.     

利用多光子相互作用实现量子信息传递

利用全量子理论,研究了多原子-腔场系统中多光子相互作用的过程,给出了不同情况下系统的一般演化式,发现利用此过程可实现量子纠缠信息的传递:只要控制腔场与原子相互作用的时间即原子以特定速度通过腔场时,处于基态的原子与存储纠缠信息的腔场相互作用的结果使原子获得量子纠缠信息;相反,纠缠原子中的量子纠缠信息也可传递给处于真空态的腔场;基态原子作为"飞行的量子比特"还可将量子纠缠信息从一个腔场传递到另一个腔场。该结论适应于讨论任意多个原子-腔场系统中任意多个光子相互作用的普遍情形。     

Quantum Fisher Information in the Generalized One-axis Twisting Model

We investigate the quantum Fisher information (QFI) of symmetric states for spin-s particles. We derive the maximal QFI, and find that quantum spin correlations are essential ingredients of the maximal QFI. We make applications to the generalized one-axis twisting model. The results show that the redistributions of uncertainties on the basis of the quantum correlations in the multiqubit system are useful for sub-shot-noise phase sensitivity. Furthermore, for high-spin (s>1/2) composite systems, we find a sufficient criterion for entanglement.     

Operational quantification of continuous-variable correlations

We quantify correlations (quantum and/or classical) between two continuous-variable modes as the maximal number of correlated bits extracted via local quadrature measurements. On Gaussian states, such "bit quadrature correlations" majorize entanglement, reducing to an entanglement monotone for pure states. For non-Gaussian states, such as photonic Bell states, photon-subtracted states, and mixtures of Gaussian states, the bit correlations are shown to be a monotonic function of the negativity. This quantification yields a feasible, operational way to measure non-Gaussian entanglement in current experiments by means of direct homodyne detection, without a complete state tomography.     

Entanglement or separability: the choice of how to factorize the algebra of a density matrix

Quantum entanglement has become a resource for the fascinating developments in quantum information and quantum communication during the last decades. It quantifies a certain nonclassical correlation property of a density matrix representing the quantum state of a composite system. We discuss the concept of how entanglement changes with respect to different factorizations of the algebra which describes the total quantum system. Depending on the considered factorization a quantum state appears either entangled or separable. For pure states we always can switch unitarily between separability and entanglement, however, for mixed states a minimal amount of mixedness is needed. We discuss our general statements in detail for the familiar case of qubits, the GHZ states, Werner states and Gisin states, emphasizing their geometric features. As theorists we use and play with this free choice of factorization, which for an experimentalist is often naturally fixed. For theorists it offers an extension of the interpretations and is adequate to generalizations, as we point out in the examples of quantum teleportation and entanglement swapping.     

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.     

Entanglement Degree of Finite-Dimensional Pair Coherent States

We study in detail the entanglement degree of finite-dimensional pair coherent states (PCSs) in terms of different parameters involved in the coherent states. Since these states are a type of correlated two-mode states in finite dimension, we use the D concurrence and linear entropy to quantify their amount of entanglement. We show that the maximum entanglement can be obtained for two and threedimensional (finite-dimensional) PCSs, and states with higher dimensions cannot attain this limit. We generalize the discussion to a superposition of two states of this class and give the maximum entangled states for even and odd finite-dimensional PCSs. In addition, we consider the entanglement degree of nonlinear finite-dimensional PCSs and survey the maximality condition. Finally, we discuss the entanglement for a class of mixed states defined as a statistical mixture of two pure finite-dimensional PCSs. Our observations may have important implications in exploiting these states in quantum information theory.     

Frustration, area law, and interference in quantum spin models

We study frustrated quantum systems from a quantum information perspective. Within this approach, we find that highly frustrated systems do not follow any general "area law" of block entanglement, while weakly frustrated ones have area laws similar to those of nonfrustrated systems away from criticality. To calculate the block entanglement in systems with degenerate ground states, typical in frustrated systems, we define a "cooling" procedure of the ground state manifold and propose a frustration degree and a method to quantify constructive and destructive interference effects of entanglement.     

Preparation and control of entangled states in the two-mode coherent fields interacting with a moving atom via two-photon process

We investigate the preparation and the control of entangled states in a system with the two-mode coherent fields interacting with a moving two-level atom via the two-photon transition. We discuss entanglement properties between the two-mode coherent fields and a moving two-level atom by using the quantum reduced entropy, and those between the two-mode coherent fields by using the quantum relative entropy. In addition, we examine the influences of the atomic motion and field-mode structure parameter $p$ on the quantum entanglement of the system. Our results show that the period and the duration of the prepared maximal atom-field entangled states and the frequency of maximal two-mode field entangled states can be controlled, and that a sustained entangled state of the two-mode field, which is independent of atomic motion and the evolution time, can be obtained, by choosing appropriately the parameters of atomic motion, field-mode structure, initial state and interaction time of the system.     

Phase Sensitivity in Yurke-Like State

We investigate we investigate the quantum Fisher information and phase sensitivity in Yurke-like state superposed by two special multi-particle states and a symmetric state with relative phase. By studying the influences of superposition coefficients and relative phase on the maximal quantum Fisher information and phase sensitivity, we reveal some entanglement properties of Yurke-like state.     

Fermi-Bose Systems, Macroscopic Quantum Superposition States and Entanglement

We study the entanglement of states of a simple Fermi-Bose system. The Hilbert space is C ² l₂ (N). An explicit expression is given for the entanglement. We consider number states, coherent states and macroscopic quantum superposition states in the product system. Explicit formulas for the entanglement are also given in each of these cases.     

Entanglement scaling in the one-dimensional Hubbard model at criticality

We derive exact expressions for the local entanglement entropy epsilon in the ground state of the one-dimensional Hubbard model at a quantum phase transition driven by a change in magnetic field h or chemical potential mu. The leading divergences of delta epsilon/delta h and delta epsilon/delta mu are shown to be directly related to those of the zero-temperature spin and charge susceptibilities. Logarithmic corrections to scaling signal a change in the number of local states accessible to the system as it undergoes the transition.     

Quantum phase transitions in matrix product states of one-dimensional spin-1 chains

We present a new model of quantum phase transitions in matrix product systems of one-dimensional spin-1 chains and study the phases coexistence phenomenon. We find that in the thermodynamic limit the proposed system has three different quantum phases and by adjusting the control parameters we are able to realize any phase, any two phases equal coexistence and the three phases equal coexistence. At every critical point the physical quantities including the entanglement are not discontinuous and the matrix product system has long-range correlation and N-spin maximal entanglement. We believe that our work is helpful for having a comprehensive understanding of quantum phase transitions in matrix product states of one-dimensional spin chains and of certain directive significance to the preparation and control of one-dimensional spin lattice models with stable coherence and N-spin maximal entanglement.     

Efficient Entanglement Concentration of Nonlocal Two-Photon Polarization-Time-Bin Hyperentangled States

We present two different hyperentanglement concentration protocols (hyper-ECPs) for two-photon systems in nonlocal polarization-time-bin hyperentangled states with known parameters, including Bell-like and cluster-like states, resorting to the parameter splitting method. They require only one of two parties in quantum communication to operate her photon in the process of entanglement concentration, not two, and they have the maximal success probability. They work with linear optical elements and have good feasibility in experiment, especially in the case that there are a big number of quantum data exchanged as the parties can obtain the information about the parameters of the nonlocal hyperentangled states by sampling a subset of nonlocal hyperentangled two-photon systems and measuring them. As the quantum state of photons in the time-bin degree of freedom suffers from less noise in an optical-fiber channel, these hyper-ECPs may have good applications in practical long-distance quantum communication in the future.     

Detecting entanglement of quantum channels

Entanglement is the crucial resource for different quantum information processing tasks. While conventional studies focus on the entanglement of bipartite or multipartite quantum states, recent works have extended the scenario to the entanglement of quantum channels, an operational quantification of the channel entanglement manipulation capability. Based on the recently proposed channel entanglement resource framework, here we study a further task of resource detection—witnessing entanglement of quantum channels. We first introduce the general framework and show how channel entanglement detection is related to the Choi state of the channel, enabling channel entanglement detection via conventional state entanglement detection methods. We also consider entanglement of multipartite quantum channels and use the stabilizer formalism to construct entanglement witnesses for circuits consisting of controlled-Z gates. We study the effectiveness of the proposed detection methods and compare their performance for several typical channels. Our work paves the way for systematic theoretical studies of channel entanglement and practical benchmarking of noisy intermediate scaled quantum devices.     

利用依赖强度的非共振相互作用实现纠缠信息的完全交换

利用全量子理论,分析了多个原子-腔场构成的联合系统中原子与腔场依赖强度的非共振相互作用过程.结果表明:通过控制原子与腔场相互作用时间,并对原子状态进行测量,原子最大纠缠态与类奇偶相干态光场的最大纠缠态可以相互转换;对失谐量的限制,使得二者之间完全交换,进一步证明封闭系统中的演化是可逆的.     

Preparation of Greenberger-Horne-Zeilinger and W states of three atoms trapped in one cavity through cavity output process

We propose a protocol to generate Greenberger-Horne-Zeilinger (GHZ) and W states of three atoms trapped in only one cavity. The setup involves one cavity and linear optical elements. The quantum information of each qubit is skillfully encoded on the degenerate ground states of the three different atoms, hence the entanglement between them is relatively stable against spontaneous emission. The advantages of the protocol are their robustness against detection inefficiency and asynchronous emission of the photons. We discuss the issue related to the practical implementation and show that the protocol is accessible within the current cavity QED technology and linear optical technology.     

Two-photon coincident-frequency entanglement via extended phase matching

We demonstrate a new class of frequency-entangled states generated via spontaneous parametric down-conversion under extended phase-matching conditions. Biphoton entanglement with coincident signal and idler frequencies is observed over a broad bandwidth in periodically poled KTiOPO4. We demonstrate high visibility in Hong-Ou-Mandel interferometric measurements under pulsed pumping without spectral filtering, which indicates excellent frequency indistinguishability between the down-converted photons. The coincident-frequency entanglement source is useful for quantum information processing and quantum measurement applications.