Gaussian entanglement of symmetric two-mode Gaussian states

A Gaussian degree of entanglement for a symmetric two-mode Gaussian state can be defined as its distance to the set of all separable two-mode Gaussian states. The principal property that enables us to evaluate both Bures distance and relative entropy between symmetric two-mode Gaussian states is the diagonalization of their covariance matrices under the same beam-splitter transformation. The multiplicativity property of the Uhlmann fidelity and the additivity of the relative entropy allow one to finally deal with a single-mode optimization problem in both cases. We find that only the Bures-distance Gaussian entanglement is consistent with the exact entanglement of formation.     

Relative entropy of entanglement of two-qubit ’X’ states

Two closest single-qubit states could be diagonalised by the same unitary matrix,which helps to find the relative entropy of entanglement of a two-qubit ’X’ state.We formulate two binary equations for the relative entropy of entanglement and the corresponding closest separable state of a given two-qubit ’X’ state.This approach can be applied to get the relative entropy of entanglement of many widely-discussed two-qubit states,such as pure states,Werner states,and so on.     

Information, relative entropy of entanglement, and irreversibility

Previously proposed measures of entanglement, such as entanglement of formation and assistance, are shown to be special cases of the relative entropy of entanglement. The difference between these measures for an ensemble of mixed states is shown to depend on the availability of classical information about particular members of the ensemble. Based on this, relations between relative entropy of entanglement and mutual information are derived.     

Relative Entropy and Squashed Entanglement

We are interested in the properties and relations of entanglement measures. Especially, we focus on the squashed entanglement and relative entropy of entanglement, as well as their analogues and variants. Our first result is a monogamy-like inequality involving the relative entropy of entanglement and its one-way LOCC variant. The proof is accomplished by exploring the properties of relative entropy in the context of hypothesis testing via one-way LOCC operations, and by making use of an argument resembling that by Piani on the faithfulness of regularized relative entropy of entanglement. Following this, we obtain a commensurate and faithful lower bound for squashed entanglement, in the form of one-way LOCC relative entropy of entanglement. This gives a strengthening to the strong subadditivity of von Neumann entropy. Our result improves the trace-distance-type bound derived in Brandão et al. (Commun Math Phys, 306:805–830, 2011), where faithfulness of squashed entanglement was first proved. Applying Pinsker’s inequality, we are able to recover the trace-distance-type bound, even with slightly better constant factor. However, the main improvement is that our new lower bound can be much larger than the old one and it is almost a genuine entanglement measure. We evaluate exactly the relative entropy of entanglement under various restricted measurement classes, for maximally entangled states. Then, by proving asymptotic continuity, we extend the exact evaluation to their regularized versions for all pure states. Finally, we consider comparisons and separations between some important entanglement measures and obtain several new results on these, too.     

A Reversible Theory of Entanglement and its Relation to the Second Law

We consider the manipulation of multipartite entangled states in the limit of many copies under quantum operations that asymptotically cannot generate entanglement. In stark contrast to the manipulation of entanglement under local operations and classical communication, the entanglement shared by two or more parties can be reversibly interconverted in this setting. The unique entanglement measure is identified as the regularized relative entropy of entanglement, which is shown to be equal to a regularized and smoothed version of the logarithmic robustness of entanglement. Here we give a rigorous proof of this result, which is fundamentally based on a certain recent extension of quantum Stein’s Lemma, giving the best measurement strategy for discriminating several copies of an entangled state from an arbitrary sequence of non-entangled states, with an optimal distinguishability rate equal to the regularized relative entropy of entanglement. We moreover analyse the connection of our approach to axiomatic formulations of the second law of thermodynamics.     

Some New Properties of Quantum Correlations

Quantum coherence measures the correlation between different measurement results in a single-system, while entanglement and quantum discord measure the correlation among different subsystems in a multipartite system. In this paper, we focus on the relative entropy form of them, and obtain three new properties of them as follows: 1) General forms of maximally coherent states for the relative entropy coherence, 2) Linear monogamy of the relative entropy entanglement, and 3) Subadditivity of quantum discord. Here, the linear monogamy is defined as there is a small constant as the upper bound on the sum of the relative entropy entanglement in subsystems.     

Secure key from bound entanglement

We characterize the set of shared quantum states which contain a cryptographically private key. This allows us to recast the theory of privacy as a paradigm closely related to that used in entanglement manipulation. It is shown that one can distill an arbitrarily secure key from bound entangled states. There are also states that have less distillable private keys than the entanglement cost of the state. In general, the amount of distillable key is bounded from above by the relative entropy of entanglement. Relationships between distillability and distinguishability are found for a class of states which have Bell states correlated to separable hiding states. We also describe a technique for finding states exhibiting irreversibility in entanglement distillation.     

Measures of genuine multipartite entanglement for graph states

Graph states are special multipartite entangled states that have been proven useful in a variety of quantum information tasks. We address the issue of characterizing and quantifying the genuine multipartite entanglement of graph states up to eight qubits. The entanglement measures used are the geometric measure, the relative entropy of entanglement, and the logarithmic robustness, have been proved to be equal for the genuine entanglement of a graph state. We provide upper and lower bounds as well as an iterative algorithm to determine the genuine multipartite entanglement.     

Fluctuations of quantum entanglement

It is emphasized that quantum entanglement determined in terms of the von Neumann entropy operator is a stochastic quantity and, therefore, can fluctuate. The rms fluctuations of the entanglement entropy of two-qubit systems in both pure and mixed states have been obtained. It has been found that entanglement fluctuations in the maximally entangled states are absent. Regions where the entanglement fluctuations are larger than the entanglement itself (strong fluctuation regions) have been revealed. It has been found that the magnitude of the relative entanglement fluctuations is divergent at the points of the transition of systems from an entangled state to a separable state. It has been shown that entanglement fluctuations vanish in the separable states.     

高斯型耦合多光子Tavis-Cummings模型中场与原子的纠缠特性

利用全量子理论,研究了多光子跃迁过程高斯型耦合Tavis-Cummings模型中场与原子的纠缠特性。讨论了多光子原子运动速度、光场初态的平均光子数及跃迁光子数对场与原子之间纠缠特性的影响。结果表明:原子运动速度的变化改变了场熵演化曲线的振荡时域;光场初态影响场熵演化曲线的周期性;跃迁光子数的增加使场熵演化曲线的振荡频率和场与原子之间的平均纠缠度变大。     

Majorization theory approach to the Gaussian channel minimum entropy conjecture

A long-standing open problem in quantum information theory is to find the classical capacity of an optical communication link, modeled as a Gaussian bosonic channel. It has been conjectured that this capacity is achieved by a random coding of coherent states using an isotropic Gaussian distribution in phase space. We show that proving a Gaussian minimum entropy conjecture for a quantum-limited amplifier is actually sufficient to confirm this capacity conjecture, and we provide a strong argument towards this proof by exploiting a connection between quantum entanglement and majorization theory.     

Entanglement of multipartite Schmidt-correlated states

We generalize the Schmidt-correlated states to multipartite systems. The related equivalence under SLOCC, the separability, entanglement witness, entanglement measures of negativity, concurrence and relative entropy are investigated in detail for the generalized Schmidt-correlated states.     

Entanglement irreversibility from quantum discord and quantum deficit

We relate the problem of irreversibility of entanglement with the recently defined measures of quantum correlation--quantum discord and one-way quantum deficit. We show that the entanglement of formation is always strictly larger than the coherent information and the entanglement cost is also larger in most cases. We prove irreversibility of entanglement under local operations and classical communication for a family of entangled states. This family is a generalization of the maximally correlated states for which we also give an analytic expression for the distillable entanglement, the relative entropy of entanglement, the distillable secret key, and the quantum discord.     

Structure formation of entanglement entropy in a system of two superconducting qubits coupled with an LC-resonator

This paper investigates theoretically the evolutions of the entanglement entropy of a system of two coupled-charge-qubits interacting with an LC-resonator.It is found that when the initial states of the two qubits are prepared in a given superposition excited state,the evolution of the von Neumann entropy of the system depends significantly on the coupling strength between the two Josephson charge qubits.With the variation of the coupling strength,the evolution of the entanglement entropy of the system forms some structures,especially the periodically bistable properties,which are the first discovered for such a system to our knowledge.It is found that the relative entropy entanglement of the system is also sensitive to the variation of the coupling strength between the two charge qubits,some novel ’collective oscillations’ of the relative entropy are found for the system.     

Gaussification and entanglement distillation of continuous-variable systems: a unifying picture

Distillation of entanglement using only Gaussian operations is an important primitive in quantum communication, quantum repeater architectures, and distributed quantum computing. Existing distillation protocols for continuous degrees of freedom are only known to converge to a Gaussian state when measurements yield precisely the vacuum outcome. In sharp contrast, non-Gaussian states can be deterministically converted into Gaussian states while preserving their second moments, albeit by usually reducing their degree of entanglement. In this work-based on a novel instance of a noncommutative central limit theorem-we introduce a picture general enough to encompass the known protocols leading to Gaussian states, and new classes of protocols including multipartite distillation. This gives the experimental option of balancing the merits of success probability against entanglement produced.     

Relative entropy of entanglement of rotationally invariant states

We calculate the relative entropy of entanglement for rotationally invariant states of spin- and arbitrary spin-j particles or of spin-1 particle and spin-j particle with integer j. A lower bound of relative entropy of entanglement and an upper bound of distillable entanglement are presented for rotationally invariant states of spin-1 particle and spin-j particle with half-integer j.     

Equivalence between entanglement and the optimal fidelity of continuous variable teleportation

We devise the optimal form of Gaussian resource states enabling continuous-variable teleportation with maximal fidelity. We show that a nonclassical optimal fidelity of N-user teleportation networks is necessary and sufficient for N-party entangled Gaussian resources, yielding an estimator of multipartite entanglement. The entanglement of teleportation is equivalent to the entanglement of formation in a two-user protocol, and to the localizable entanglement in a multiuser one. Finally, we show that the continuous-variable tangle, quantifying entanglement sharing in three-mode Gaussian states, is defined operationally in terms of the optimal fidelity of a tripartite teleportation network.     

Revised Geometric Measure of Entanglement for Multipartite and Continuous Variable Systems

Based on the revised geometric measure of entanglement （RGME） proposed by us [J. Phys. A： Math. Theor. 40 （2007） 3507], we obtain the RGME of multipartite state including three-qubit GHZ state, W state, and the generalized Smolin state （GSS） in the presence of noise and the two-mode squeezed thermal state. Moreover, we compare their RGME with geometric measure of entanglement （GME） and relative entropy of entanglement （RE）. The results indicate RGME is an appropriate measure of entanglement. Finally, we define the Gaussian GME which is an entangled monotone.